Hi Peruman,
I agree, I think your problem could be in the player unit. The schematic snippet I've attached is for the "Ball in Play" lights. On the player unit, it looks like positions 1, 5, 9, 13 and 17 are where the contact should be when player 2 plays each ball, and that should light the appropriate "ball in play" light. Assuming there's not a broken wire somewhere in the circuit, it looks like the path to light the ball in play has to go through the player unit, and through switches on Q, AX and P (in the lower left). But the fact that the ball in play light IS working for player 1 means that either one of those 3 switches on Q, AX or P is changing states (opening) when player 2 is up, or possibly there's a bad connection on the player unit involved with player 2.
To start attacking this, I would watch relays Q, AX and P while player 1 is up, see if they're in the same state for player 2, and if so, then look carefully at the wiring/solder connections in the player unit.
I wonder too, if the rotating disc on the player unit that has the spring-loaded snowshoe contacts could be off by 1 rivet. I don't know how likely that would be, but it wouldn't hurt to check.
I don't understand all the ins and out of the player unit circuitry myself, so if it gets more involved, maybe someone more knowledgeable can chip in. Good luck!