Do either the Clutch Trip relay or the Ball Return relay fire after you hit the start button?
Gator Reset motor (resized).jpg
I think one of those two should get the Reset Motor started. Note that the Ball Return relay won't fire unless the Outhole switch is closed.

/Mark

Agreed. But of the five possible switches that could start the Reset Motor during reset the one on the Ball Return relay feels most likely to me. Free Ball doesn't seem like a reset thing, and the other switches appear to be dependent on the Reset Motor turning already.

Just for grins, here's the Ball Return relay circuit:
Gator Ball Return relay (resized).jpg
Note that in addition to the Outhole switch it is dependent on switches on the the Start, Game Over and #3 Reset relays. The #3 Reset relay should trip once all the score reels reach zero. Does it? Do all of the switches to the Ball Return relay close when the game is stuck in reset?

Just so we're on the same page, did you check the resistance across each switch in the Clutch Trip relay path individually, or across the compete circuit as shown here:
Gator Clutch Trip relay (resized).jpg
If you checked switches individually the problem could be in the wiring, or through a connector etc. Checking the resistance across both legs of the entire circuit while manually activating the devices that should close the switches would be a little more comprehensive. You should be able to measure an ohm or so across the path shown when all of the switches on either leg are closed.

Another test would be to put your (preferably analog) multimeter across the solder lugs of the Clutch Trip relay on AC volts and see if you get an AC pulse during reset. You probably won't be able to measure the value, but seeing it jump from 0 volts would indicate whether it's getting anything. Alternatively you could string together four 12 volt turning signal bulbs in series and wire them in parallel with the Clutch Trip relay to see if they flash during reset. This is essentially Steve Fury's light bulb tester described elsewhere in this forum.

The Flippers.com resistance chart shows the Clutch Trip relay should be 6.3 ohms, or the same as the Game Over Trip relay next to it on the schematic above.