the trough switch is just a switch in a circuit that grounds the P relay, Which in turn gives a path to ground for P. The motor is wired direct to ground but if you look at schematic there are switches on different relays that are listed that close and ground the motor (which turns it) The motor is wired to make a 1/3 revolution turn. The state of switches shown in schematic are ball in shooter lane, game unplugged. Every coil is wired hot. It is the path to ground that controls the logic. Different relays switches isolate others. Just follow the left side (hot) to the right side (-). All coils have the black wire on one side. That is the left side of schematic. on the other side of coil is the path laid out in the schematic. I repeat again and again- the state of the machine in this schematic (snapshot) reset complete, ball shot into shooter lane, game turned off.
The add player coil on schematic is the coil on the player unit. The ground path straight across thru P5 is the reset path that keeps the unit advancing thru the startup. P5 switch drops this path out after reset for the entire gameplay. The other path to ground is down on schematic thru a switch on P. remember P is grounded by the ball passing trough switch. The path goes thru a motor switch position 2 stack c (motor is turning because of a motor switch on P) the circuit then gets blocked by the switch on first ball relay. This switch is opened and blocking the path because no points have been scored yet, so this relay should not be tripped yet. After points are scored the switch will close and open the circuit to fire the player unit coil each time a ball passes trough switch. The game over switch is the last switch in the path and it will open and block the circuit when game over relay is tripped.
Your problem may involve the first ball relay. When the ball kicks out before any points are scored a switch on this relay should block the coil on the player unit from advancing any.