You are correct, this is the lock-in switch for the 10-point relay. The four EOS switches, which are all normally closed, are located on the four 10-point score units (one EOS switch per score unit). When any of the 10-point score units indexes, its EOS switch will be pushed open, allowing the 10-point relay to release.
Since none of your 10 point score units are indexing, none of the EOS switches ever open, so the 10-point relay stays locked on forever once it is energized. Bending the lock-in switch on the relay so it never closes "fixes" this infinite lock-on problem, but it doesn't get the 10-point score units working.
In the head of your game, there is a player-up stepper unit. This stepper is fairly easy to identify because it has a bunch of wires attached to the many wiper fingers that are on the stepper. These wiper finger wires are routed back to the stepper disc inside a spring, which protects the wiring.
The player-up stepper only has four positions. Each position selects which score units will receive the scoring from the playfield. When the stepper is reset, player 1 is selected. Step it up once, and player 2 is selected. Step it up once more, and player 3 is selected. Step it up one more time, and player 4 is selected. After that, the stepper won't advance any more.
The wiper fingers contact a different set of rivets on the stepper disc at each position, and it is this connection that determines which set of score units will receive the scoring. So if none of the 10 point score units work, I would suspect there is some failure with the 10-point wiper finger connection to the rivets. Either the finger is bent and not touching any rivets, or there is a broken wire at one of the solder joints (either on the wiper finger or at the disc), or something like that. So I recommend you look at the player-up stepper in the head and see if you can find anything out of whack there.
- TimMe