Okay... sorry about the delay.
Of course I don't need to tell you, do I? ... that it worked just fine when he got here.
But even so... here are the things he looked at: The coin relay (which I never looked at) the player unit (which I looked at over and over) and also a sets of motor points that step up the player unit (which I had checked and cleaned before)
But the thing he thought was the CULPRIT... was the plunger on the coil that resets the player unit back to player one when starting a game. It was very sluggish when it operated. I had noticed this and thought I addressed this issue by spraying some good lubricant on the plunger and also the arm that goes into this slotted plunger. But apparently that didn't do the trick. He took the arm off the shaft and cleaned it really well inside and also the shaft itself. Which is something I should have done but didn't. There were also four springs on the stepper when there should have only been two. Someone before I owned the game tried to fix the problem in this manner and I didn't catch it.
The world's oldest fledgling tech fails again.
Anyway, when HE got done with it, the game resets to player one now as it should and I haven't had the problem since.
You just can't beat experience.