the mystery of player #3

Remember those logic puzzle grids they gave you in elementary school?  you'd have to cross-reference clues and make deductions based on the info at hand to solve the chart and connect all of the proper assignments.
An electro-mechanical (EM) pinball machine is kind of like that.  The functionality is laid out in a straightforward schematic that a human can actually digest and, with some effort, trace cause-and-effect through.

Most EM problems do not require this.  As has been said by people much more talented than myself, a systematic EM overhaul will solve 80% of all problems.  Clean, lube, adjust, and do it all with patience and love.  My last issue, which resulted in a month of downtime most likely due to my lack of diligence in TRUSTING THE METHOD, could have probably been solved with a loving hour of a knowledgeable EM tech following the system.  But I think I have a problem that isn't quite so elementary.  (but who knows, perhaps I speak too soon.)

THE PROBLEM...


Player #3 runs everything.  If I set a 3 or 4 player game, once we get to player 3 the player unit never progresses.  When we get to player #3 something... happens.
It's a bit of a mystery.  And I've done some troubleshooting, and I want to lay out the clues so I have them handy for cross-referencing and deducing who is the real killer problem switch...

When player #3 ball #1 drains, the player unit fails to advance.  Ball is ejected in to shooter lane, player #3 ball #1 continues indefinitely.
When only a 1 or 2 player game, player unit steps perfectly through entire game and subsequent game.

When we hit player 3, then we turn the game off, and on again, the AX relay must be manually unlatched and then the player unit must manually (via stepping the solenoid) stepped through each position.  Once it hits the 2nd reset position it takes off on its own and is then ready for a new game.
With just 1 or 2 players, when we turn the game off then on everything is perfect and no manual intervention is required.

When we hit the player#3 problem (as it will be herein be referenced,) I then manually step the player unit to play some of a proper 4-player game.  I decide to turn the power off while set on player #1 ball #3.   with power-on, the manual intervention of AX + player unit stepping is required.  (well, technically I don't know if the AX resetting is really required...  I should test that)
This shows to me that it is not the physical position of the player unit that is resulting in this.

I also ran a test, taking the game to player #3 ball #1, turning it off then on, and no issue.  The issue ONLY arises when player #3 ball #1 ends, and the game fails to progress to the next player.   Progression fails, ball is in shooter lane, off then on and yup, stuck.


There is ....  SOMETHING lingering.  Something that lingers during power reset.
I think the AX/BX relays the only relays that retain a state during power on/off.  The player unit maintains its' position.  But even if I make sure AX and BX relays are reset, I am still forced to manually progress the player unit to its reset states.  I also verified that the coin unit resets fine at power on.

Any ideas?
It's not the play unit position, not the coin unit, it's not the AX/BX relays...  WHAT ELSE IS THERE?