game over light needs the game over relay (Q) to be tripped ... that should happen at power on via a hold relay (R) switch. The AX relay (reset control relay) also needs to be reset/latched, which it probably isn't if the game is in an odd state where reset didn't complete. I wouldn't worry about the game over light behavior when reset state is ambiguous.
is the player unit ever stepping without doing it manually? For example, when you reset and the player 1 score reels zero, the player unit needs to step before the player 2 score reels will zero.
also, keep in mind different switches on the score reels are used to for reset. The wires with the red tracers on the runout switches in pauls schem above stop each reel from stepping when it reaches zero. The reel switches with mostly WH wires connect in series all need to be closed (for each player) to complete the circuit to step the player unit. This is what bronx is talking about above, so I guess it's the bottom switches you need to ensure are closed when the reels are zero.
i.e. if you find the reel switch on the player 1 tens unit with the OR-WH-RED wire connecting to a WH-GR wire and stick an ohmeter probe there, you should see zero ohms on the BR-WH-RED wire on the player unit step-up coil when the player 1 reels are all zero AND P3E switch is open. If you don't, one of the reel switches is open so the player unit never steps and the reset sequence stalls.
player unit diagram below.
surfers_player_unit (resized).png
player unit step-up circuit below. If the reel switches are good but player unit is dead, you gotta check the path thru P4E (or all player 2 reels zero), motor 1A, S/P5B and the AX relay switch. The player unit coil could also be bad.
player unit stepup (resized).png