I was puzzling over the obvious question of "What happens in the game in ball #3 that is unique to it, and will also retain it's problem state at power on?" the answer, of course, THE SCORE REELS!
Yes, once ball #3 is in play, player #3's score is now non-zero.
Here is the player-unit-advance schematic: (click to embiggen!)
the upper sections are for the reset process. Z1 and Z2 have NC switches that allow for normal operation when the game is playing. When Z1 activates, all reels for Player 1+2 need to get to reset position before the player unit can advance (and Z1 is deactivated). Then Z2 activates, opening the NC switch, and then Players 3+4 score reels need to get to zero before the player unit can advance.
In a normal 1 or 2 player game, the score on players 3 and 4 stays at zero. But once any points are scored on player 3, suddenly the path of "3rd player reset switches" is blocked.
Normally the circuit would go through the NC Z2 switch, but this is where are system was having problems, and yes it was the switch on Z2 that wasn't closed properly.
I tightened the screws, got out the flexstone file, bent the blade inward, and voila, that Z2 switch is now normally closed properly.
Here is a glimpse of it before adjustment:
|far right at the top, you can even see the gap between the contacts. Fix that ish!|
Problem solved, player a full 4-player game of Royal Flush! ON TO THE NEXT CHALLENGES!