Let's start with something simple.

Tha Advance Unit advances one step when its Step Up (SU) solenoid fires:
Doodle Bug Advance SU (resized).jpg
That can happen in two situations. The upper line of the schematic shows that a switch on the Advance relay can fire the step up solenoid. The lower line shows that a switch on the Eject relay combined with a switch on the Score Motor can fire the step up solenoid. If your eject hole doesn't change the Advance unit check to see that the Eject relay fires, the Score Motor turns and that both switches close. Visually closing may not be good enough. You'd want to check with a meter or bulb tester to be sure that when they're closed current can flow through the switches.

You mentioned the schematic but there is also a manual on ipdb.org that explains the step units and relays in detail. In particular it shows the Match Unit. If you suspect the Match Unit is giving you trouble you might carefully compare it to the diagram in the manual. It's possible that the wiper arms were removed at some point and installed 180 degrees from where they should be.

In addition to the many good online resources the original Williams Intro to Coin Operated Amusement Games would be a good thing to read through. Links to it and similar documentation are at https://www.funwithpinball.com/resources/parts-catalog-list-page-2#Williams

/Mark

Go to the Doodle Bug page on IPDB (https://www.ipdb.org/machine.cgi?id=703) then scroll down through the text to just before the image section. There is a Documentation section that includes links to the catalog supplement, manual and schematic.

You confirmed that the Eject relay fires, or that the switch to the Advance Step Up coil closes? The Eject relay has half a dozen Normally Open (N.O) switches that all do different things. The one that should fire the Advance Step Up solenoid is highlighted in red in this section from the manual:
Doodle Bug Eject relay (resized).jpg
The manual shows you where the switch is in the switch stack, what its wire colors are, where to find it on the schematic and explains what it does.

A switch on the Advance relay is one of the two ways that the Advance Unit Step Up solenoid can fire as shown in the schematic above. The Advance relay and Advance Unit are different things. The Advance Unit is a big step unit pictured in the manual. I think we're assuming that when the Advance relay fires the Advance Unit takes a step. That leaves the other path through the Eject relay switch shown earlier to troubleshoot.

There are several ways to troubleshoot a circuit described elsewhere in the forum. If you're new to troubleshooting and only have a meter a resistance check is a safe way to go.

First unplug the game. Then clip your meter probes to the green-black and grey-black wires on the solder lugs of the Eject relay switch highlighted above. Put your meter on the lowest resistance setting and read the resistance value. It should be some high value or possibly something like "Overflow". When you manually activate the Eject relay by pushing in on the plastic armature all of the switches will close including the switch you're testing. With the switch closed your meter should read something like 1 ohm or less. That indicates that there is very little resistance between your meter probes, or that the switch is closed. Repeat activating and releasing the relay to convince yourself that it reliably opens and closes the switch. If it doesn't chances are that the switch contacts are dirty, the contacts don't touch, or a wire has broken free or there is some other issue that keeps the switch from closing.

Once you've got the Eject relay switch reliably working move your meter over to the Score Motor switch and do the same test. Once your meter is clipped in, manually rotate the Score Motor in the same direction it turns during the game and watch as the profile of the cam opens and closes the switches in the stack. Convince yourself that the Score Motor 1B switch opens and closes.

For extra credit clip your meter to the yellow wire on the Score Motor switch and to the grey-black wire on the Eject relay switch and repeat the test with both switches between the meter probes. That should demonstrate how both switches need to be closed before that path can fire the Advance Unit Step Up solenoid.

/Mark

Switches are only effective if they can electrically (not just visually) change state between open and closed. A switch that can't open or close wouldn't be in the circuit because it can't accomplish anything. Beware though that you can't assess switches in isolation. You need to check how they're being used in the schematic. If the meter indicates that your switch isn't opening for example you need to check that there isn't another normally closed switch wired in parallel with it.

This is a mechanical issue that needs to be resolved before you spend much time troubleshooting. Read up on cleaning step units. If your stepper is sluggish as it takes steps or resets it likely needs a good cleaning. If it's snappy and still lands between contacts the wipers could be mangled or the contact board might be out of position.

I don't usually evaluate every switch unless I'm doing a complete tear down restoration. If you're just troubleshooting focus on the issue you're trying to resolve. Find the hand full of devices in the small part of the circuit that's relevant and inspect them carefully, dismissing each as a possible culprit as you go. If you find something suspicious that's unrelated make a note and come back to it later.

There's another learning opportunity coming up later this week:
https://pinside.com/pinball/forum/topic/an-em-pinball-online-repair-clinic/page/2#post-5823646

Different Mark. My stuff is all on my website at https://www.funwithpinball.com/

Do you mean that the Reset relay doesn't let go? The Reset relay stays active until it thinks that the game reset has completed.
Doodle Bug Reset relay (resized).jpg
Once the Reset relay is activated by a switch on the Coin relay (for example) it will hold itself active through its own holder switch until the four Drum Unit (or Score Reel) Zero Position switches open indicating that the Score Reels have reset to zero.

If you block the Reset Relay switch with a piece of paper and the Reset relay doesn't stay on the issue is either with the Zero Position switches or the Make/Break Score Motor Index-A switch.

I don't follow your experiment.

The reset sequence from the start should be:
- press the replay button
- replay button switch fires the Coin relay
- a switch on the Coin relay fires the Reset relay
- a switch on the Reset relay starts the Score Motor to reset the Score Reels among other things
- once the Score Reels reset and their zero position switches open the Reset relay should relax
- etc.

Sounds to me like your stuck on getting the Reset relay to relax. Do the Score Reels reset? When the Reset relay is stuck on and you slip a piece of paper between the contacts of the Reset relay switch in reply #10 (blue-brown wire to blue-white wire) does the Reset relay relax? If so that's the path that's holding the Reset relay on and the issue is one of the switches to the left (in the schematic) of the Reset relay switch you blocked.

If you think the Score Motor is running for some other reason you could block the switches that lead to the Score Motor to see if one of them is supplying power to the Score Motor.