There's a lot to unpack here. One thing at a time...

This sounds like two problems:
Cue Tease Replay reset (resized).jpg
First the Credit or Replay unit should stop resetting once it reaches zero credits. Check that the zero credits switch opens once the Replay unit reaches zero and that it's not somehow shorted by bent solder tabs or whatever.

Next it sounds like either the Start Trip relay or 2nd Coin relay is stuck on, or one of the switches shown above on those relays is stuck closed. I think these two should stay on for a score motor cycle and then relax once the game starts resetting. If the Start Trip relay is stuck on, check if the 25 Cent relay is stuck on too.

Beware that the Start Trip, 2nd Coin and 25 Cent relays are all in the 120 volt part of the circuit so observe them carefully and don't touch anything unless the game is unplugged.

/Mark

First a little nomenclature to make sure we're talking about the same thing. Without access to the game I'll assume that the Game Over Trip relay is a trip relay, meaning that it should trip when the game ends, and is mechanically reset at the start of the game by the large Trip Bank Reset solenoid that resets all of the trip relays in the bank at the same time. For those unfamiliar, most relays including the Game Over Trip relay should operate on momentary pulses and should not stay active or get warm.

Here is the schematic for the Game Over Trip relay on Cue Tease:
Cue Tease Game Over relay (resized).jpg
For the Game Over Trip relay to stay active due to its own circuit would require that 3 normally open switches on the left part of the circuit, or 2 or 3 normally open switches on the right side of the schematic all be stuck closed. Not impossible but somewhat unlikely. It seems more likely that there is an unrelated short connecting the 40-0/green wire on one side of the relay coil to the 15-3/red-yellow supply wire at the top of the schematic.

To prove whether or not a short exists you could block a switch from each side of the circuit, for example the switch on the Match relay and the switch on the 1st Player Tilt Trip relay. Also unplug the Match Feature Adjustment jones plug to remove it from the circuit. If the Game Over Trip relay still fires there must be another path to the relay coil that's not on the schematic and is probably a short.

Finding the short will take some investigation. If you're lucky the short is always there. If that's the case you can unplug the game and clip your meter between the green wire and the red-yellow wire and measure an ohm or less of resistance between the two. If you can measure an ohm or less with the game unplugged then start poking around to see if anything you touch or wiggle changes the resistance. I'd start by examining the solder lugs of the trip relay switches and trip relay coils. Notice how two of the switches on the right side of the schematic are also in the trip relay bank. It could be that there are some bent solder lugs that are touching each other.

So the game resets including all the trip relays, and the Game Over Trip relay immediately starts heating up because it's being powered? And it doesn't trip even though it's powered?

If you block those switches, does the Game Over Trip relay coil still get power and get hot? If so power is likely coming from a short not shown on the schematic.

This is suspicious but inconclusive. I'd expect to see more resistance. What's the resistance of the coil itself? I'd expect it to be more than that even if measured in circuit. Either way, the resistance from green to red-yellow wires should be at least as much as the resistance of the coil. If it's less that would indicate that there's another path to the coil around the switches you blocked.

The 1B SCM switch in the schematic above is on the score motor. Perhaps there's a short near that switch?

There is a description of the reset sequence in the An Introduction to Bally Flipper Games manual that may be of some help:

Link at:
https://www.funwithpinball.com/resources/parts-catalog-list#Bally
or directly at:
http://www.backglass.org/williams/kordek_archives/introduction_to_bally_flipper_games_blue_cover_100.pdf

But without the game or a game manual the specific reset sequence for this game may be hard to find. It would be possible to figure it out from the schematic but that is a big job. Are there one or two things in particular that aren't working?

To elaborate on @howardr's question there are a couple of likely causes why none of the score reels reset if the score motor is turning:
Cue Tease Score Reel reset (resized).jpg
If the Reset Trip relay isn't in the right position during reset none of the switches (in the long red box) that provide a path from the score motor to the score reels will be closed.

Another possibility is that the Score Motor 1A switch (in the small red box) isn't closing to provide reset pulses to the score reels.

Either way the Score Motor will likely keep turning until all the score reels reach zero.

Maybe you're all over this but for anyone else reading who isn't familiar, continuity isn't what you're looking for when you're testing switches. Depending on the meter continuity can be anything lower than 20-30 ohms of resistance. What you really want to see when testing a switch is that the resistance drops from whatever it is when the switch is open to about an ohm or less when the switch is closed. If the resistance is 20 ohms for example when the switch is open there could be a path through a coil somewhere and not through the switch and your meter might still report that there is continuity.

I'd poke around a little more with your meter to see if you can determine why the score reels don't reset even though the motor turns.
Cue Tease Score Reel reset 2 (resized).jpg
Unplug your game and clip one meter probe to the solder lug with the 18/red-black wire on the 1 point Score Reel for Player 1 shown as A above. Clip the other probe to the 45/green-white wire on one of the switches on the Reset Trip relay shown as B above. Set the meter to measure resistance on its lowest setting. Then manually trip and reset the Reset Trip relay. If the score reel isn't at zero you should see the resistance go between an ohm or less and something much higher as you move the relay between its two positions. That would prove that there's a good path between the two wires.

If that test is successful, move the probe from the 45/green-white wire (B) to the 30/yellow wire (C) on the Score Motor 1A switch. Leave the other probe at A. Turn the Score Motor manually until the 1A switch closes. Then manually trip and reset the Reset Trip relay again. You should see the resistance again change from about an ohm or less to something much higher. That should prove whether the three switches that are needed to get the 1 point Score Reel of Player 1 to reset are working.

Zero is what you'd expect (open circuit). During reset each Score Reel needs to stop at zero so the switch opens to keep any more pulses from getting to the Score Reel coil. The rest are probably ok. The variability is likely due to varying amounts of dirt between the switch contacts in slightly different positions.

That's probably your problem. 72 ohms is likely more than the resistance of the Score Reel coil so when all three switches close the coil sees less than half of the 50 volts it should see. That could also explain why none of the Score Reels reset. While you'd expect to see an ohm or less across one closed switch, you should probably see less than two ohms across three closed switches. Start probing along that circuit (between C and A) to see if you can narrow down where you're picking up the extra 70 ohms. If you're lucky the Score Motor 1A switch is just really dirty or making poor contact.

You measured the resistance between A and B with the two switches between them closed and it was about right (~1 ohm). When you measured the resistance between A and C with the three switches between them closed you got 70+ ohms. So somewhere between B and C you picked up a lot of resistance.

If you measure the resistance between B and C what do you get with the Score Motor 1A switch open and closed? What if you move the probes to different places along the same wires? What if you wiggle the switch leaves or the wires involved? Does any of that affect the resistance?

Don't rely on just a visual examination. Even if the contacts are clean you could have loose contact points, a cold solder joint, a broken solder tab, too little tension on the switch contacts, etc. Let the meter tell you how good the connection is.

Setting the Score Reel to zero should open the zero position switch breaking the path to the Score Reel coil. If you measure resistance from A to one of the other points you'll want that switch closed. If you're measuring from B to C the zero position switch won't matter.

If your resistance from A to C with all three switches closed went from 70+ to 1 ohm, then I think you sorted it out. Try it.

Is it constantly on, or is it pulsing on and off as the the Score Motor turns? If you remove the ball from the trough does the ball release stop operating?

There are nine switches that can cause the score motor to run:
Cue Tease Score Motor (resized).jpg
Each one can connect the 30/yellow wire to the 13/red-yellow wire to send power to the Score Motor. Which ones are closed? If you're not sure, put a piece of folded paper between the contacts on each switch and then remove them one at a time.

In the previous problem we were looking for a reason why something wasn't getting power. That's why we used the meter to chase the resistance. Here the Score Motor is getting power so we need to figure out which of the 9 switches is providing power to it. A visual check or blocking switches with paper should suffice initially.

You mentioned that the Reset Trip relay switch is normally closed. Does the Score Motor stop if you trip the relay so the switch opens? The problem could be that the Reset Trip relay never trips.

Is that a typo? If the relay changes position but a switch activated by its armature stays open in both positions the switch isn't working and probably needs to be adjusted.

Back in the original post you said:

Is that still true? If you manually reset the trip relay bank by pushing in the large solenoid plunger does the motor stop?

Studying the schematic some more I think the order of events should be:
- the game powers up idle with the Reset Trip relay already tripped from the previous game
- pushing the Replay button (if there's credit), or dropping a coin should trip the Start Trip relay
- the Score Motor should start turning because a Normally Open switch on the Start Trip relay just closed
- the Trip Relay bank should reset, latching all of the trip relays including the Start Trip and the Reset Trip relays
- the Score Motor should keep turning because a switch on the Reset Trip relay has closed
- The Reset Trip relay should trip (once the Score Reels have reset to zero) and the Score Motor should stop

If your Trip Relay bank isn't resetting your Score Motor is probably running because the Start Trip relay switch is closed.

That should be easy, there are only three switches that need to close for the Trip Bank Reset solenoid to fire:
Cue Tease Bank Reset (resized).jpg
Unplug the game first because these all run at 120 volts. Then check all three switches to see that they're clean and can open and close properly. For extra credit check your work with your meter as described in reply 22.

There's resistance between your meter probe and whatever you touch it to. How much resistance will depend on how much dirt, corrosion, oxidation, etc. there is on whatever you're probing. That's why the absolute values aren't as important as how much the resistance changes when switches open and close.

You didn't say. Do the three switches in reply 45 all open and close properly when you mechanically operate the motor or relay that activates them? (Remember, with the game unplugged.) And what about the reset sequence from reply 42?

Something's wonky with your left coin chute, and your game may not be set for free play so the replay button might not do anything. But the right coin chute seems to be doing the right thing. What happens if you set the score reels to something other than zero and activate the right coin chute?

Sorry, I don't follow. You said the score reels reset and the Reset relay trips. Is that right? Can you clarify? How far through the reset sequence can you get in the best case? What happens once that has completed (what works, what doesn't work, does the motor stop, etc.)?

Or maybe start a new topic with a complete description of where you are. You'll probably get more help with a new topic.

That's unlikely the case here because there are both normally open and normally closed switches in series with the Score Motor. If that were the case then the Score Motor would be running once the ball is served up before any points have been scored.

Rather than trying to keep track of normally open or normally closed switches it may be easier to think about when the Score Motor needs to run. All but one of the switches that can power the Score Motor are normally open. That just means that the Score Motor runs *when* the switch closes. So for example the Score Motor runs *when* the 50 pt relay, or the 25 cent relay or the Start Trip relay fire.

One switch, on the Reset Trip relay, is normally closed. That means that the Score Motor runs *until* that switch opens. In this case that means that the Score Motor runs *until* the Reset Trip relay trips. (Note also that trip relays are often referred to as latched and tripped rather than latched and unlatched.)

It seems that you have trouble getting the Start Trip relay to trip with the coin chutes or replay button. Let's treat that as a separate problem and skip over it for now. I still don't have a clear picture of what's not working with the reset though. If you manually trip the Start Trip relay with a wooden dowel or something else that's non conductive, does the game reset properly? If not what doesn't it do? Keep in mind that after resetting the score reels some games need to see the ball trip over a ball trough or similar switch to supply power to the flippers and scoring switches. So reset might not finish on its own if the playfield is up unless you make the game think there are balls ready to play.

https://en.wikipedia.org/wiki/Switch#Contact_terminology