Quoted from paulace:

It sounds like your A (Reset Completed) Relay is staying in the wrong position intermittently.
When you start the game, the A relay should get a pulse through a m/b switch on the S relay to energize. That closes A switches that allow the score reels to turn until they get to zero. Once they all reach zero, the A Reset relay should fire. That's an interlock relay, so the A relay relaxes then. The switches for A should then be as shown on the schematic. The O relay then fires, which fires the Ball Kicker coil to start the game.
If the A relay isn't firing early in the process, then I think the ball would get kicked out early and you'd see what you're seeing. I'd check that m/b switch on S (highlighted in yellow) again or the Motor 2C switch next to it on the schematic. Make sure that A relay is being energized early on.
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Quoted from paulace:

It sounds like your A (Reset Completed) Relay is staying in the wrong position intermittently.
When you start the game, the A relay should get a pulse through a m/b switch on the S relay to energize. That closes A switches that allow the score reels to turn until they get to zero. Once they all reach zero, the A Reset relay should fire. That's an interlock relay, so the A relay relaxes then. The switches for A should then be as shown on the schematic. The O relay then fires, which fires the Ball Kicker coil to start the game.
If the A relay isn't firing early in the process, then I think the ball would get kicked out early and you'd see what you're seeing. I'd check that m/b switch on S (highlighted in yellow) again or the Motor 2C switch next to it on the schematic. Make sure that A relay is being energized early on.
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Quoted from dpk27:

I agree with this explanation. I had the same issue on my Top Card. The A relay was a challenge to adjust properly.

Quoted from EMsInKC:

That has to be one of the most common Gottlieb issues ever, excepting maybe the ball trough shooter not doing its job correctly.

Quoted from paulace:

Well, the fact that you changed things slightly for the better probably means you're on the right track.
I'm curious if you press in the A relay with your finger before you start a game, do the score reels reset and the game start correctly every time? If so, the switches on your A relay are probably OK - it's that the A relay is sometimes not getting the signal to fire at the start of the game. It looks like the path to fire the A relay just goes through the m/b S switch and the Motor 2C switch. I'd focus there - make sure those contacts are clean and attached firmly in their leafs, all solder connections are good, you have continuity along the wire lengths.
You could also jumper each of those 2 switches individually and see if the game starts normally if either is jumped...might give you a clue.
How do you clean your switch contacts? Sometimes, when I use an abrasive stick, a little grit can be left on the contact that makes electrical connection intermittent. I've taken to using the Dremel brush dipped in alcohol, if you have one of those....leaves a really smooth, clean contact. On the S relay, you'll probably have to take the switch stack apart to get the brush between the contacts, but you can probably do it on the Motor 2C stack with that one in place.
Then tighten the stack screws and bend the shorter leaf where it comes out of the stack for good contact. I've seen you around here for a while, so I'm sure you know all this stuff - just making sure to cover the bases. Good luck! Let us know what happens.

Quoted from dgAmpGuy:

The latching A relay can be tricky (but not as bad as the AX/BX ones).
There’s a picture and a couple of paragraphs about it in Clay’s guide, here, http://www.pinrepair.com/em/index3.htm#reset
I would check the latching plates on yours. Make sure that there are no burrs, dirt, old gunk, etc. Also, make sure that the switches aren’t over adjusted such that they fight the latch/unlatch process.
I had sort of the opposite problem on our king pin game. The latch was barely caught, so I’d have cases where it would come unlatched during the game and reset the score to zero
You seem to be on the right track, good luck.
Dave

Quoted from DaMoib:

The Start relay has a switch that should start the motor directly - the switch with RED-WH and YEL-RED wires. The Start relay will release on Motor 2B, once the motor turns.[quoted image]

Quoted from DaMoib:

The Start relay has a switch that should start the motor directly - the switch with RED-WH and YEL-RED wires. The Start relay will release on Motor 2B, once the motor turns.[quoted image]

Quoted from paulace:

For what it's worth, when it's time to adjust Gottlieb relays, I get out my magnifying glasses, a couple strong lights, a small piece of white paper, my Dremel tool and switch bender, and go at it methodically. I usually unscrew the switch stacks one at a time (unless they're wired together), get my Dremel brush in there to really get those contacts shiny, then put it back together, tighten the stack screws, examine the tabs for shorts/bad solder joints. Then while manually moving the armature up and down, I watch the contacts really carefully with my magnifying glasses on, a slip of white paper behind the switches, and a bright light (on the paper, not on the switches), I can easily see if the contacts are touching and sliding past one another slightly, then opening, or vice versa. It takes some time, but if I'm really careful about it, I don't have much trouble with them once I'm done.
As dgAmpGuy said, those AX, BX, CX relays are about the worst since there's so little movement on the armature, but even those - once you get them dialed in, they work for quite a while. And getting to some of those stacks on the bottom/back of the score motor is a pain...
I do some work for a local arcade here in town repairing the EM pins and rifle games, and after I've gone through those switches like that, we don't have much trouble with the EM's...they're mostly Gottliebs and once you get the switches cleaned and gapped, they're tanks. The SS pins on the other hand....
You'll get this - just look at everything really closely and be patient.
I only got to play a Top Card once - really liked it much better than I thought I would just looking at the playfield...clever ruleset! I enjoyed trying to get those pop bumpers lit up!