The Player Unit is likely a stepper with two solenoids. One advances the stepper from player 1 to player 4 and the other resets it to player 1. With the power off push the reset solenoid plunger all the way in and let it go. Then do the same with the advance solenoid plunger. The wiper arms should step cleanly from one set of contacts to another every time without hesitating or landing between contacts. It could be that your Player Unit has a mechanical issue in stepping from the reset/player 1 position to the player 2 position. See if it can reliably do that without power.

/Mark