Years back, I had a short problem with a Top Score, so I ordered a schematic and
figured the cross over in a switch stack in the head. Somehow, someway, a switch
stack insulator failed. There was continuity from one switch to another where an insulator
should have been preventing that from happening. I went through that stack and fixed
the problem. I had the same problem with a ball bowler's Score Motor wiper. The insulator
failed. I have a Grand Prix set up, but no schematics. If you find that the 500 point relay
impulse switch is in the same stack as the #3 Reset Relay's, that's maybe where I would
consentrate on next..

Are you saying that the #3 Reset Relay activates only on that switches' 5th pulse,
but not on it's first 4 pulses?
Yes, when the Right and Left Bonus Relays aren't energized and their switches in that
circuitry is open, indicates that the problem is between there, and the #1 Star Relay.
Do you have any questions on any of the sets of switches that I can check in my machine
that may help? Pretty sure I don't have schematics, but I'll check..

Yup, I first stated that if the 500 Point Relay was in the same stack as the #3 Reset Relay,
but should have said the 100 Point Relay which it is in the same stack..
Like you said, the problem appears to be between the #1 Star switch and Bonus Reset
switch which points right to that switch stack..
Faulty flat insulator, tube the screw goes in, or maybe even a thin tiny foreign metal stran..