I did a post on this mechanism a little bit ago that explains player number/ball number workings:

https://pinside.com/pinball/forum/topic/williams-player-unit-coin-unit-interaction

It looks like Grand Prix uses the same mechanism for that function as the game I was working on so the schematic I drew is relevant. I'd look carefully at your Coin Unit - see if all the spider fingers are making good contact and that it's moving. It should move to one of four positions as you add players before the game, and then not move during the game.

If the Coin Unit is good, look at the circuit that fires the Player Reset Relay coil....perhaps that Ball Count Unit E.O.S. switch. The Player Reset Relay coil should fire after the last player's ball drains.

After thinking about it a little more, there are several things that have to be working in order for the machine to go from Player 4, Ball 1 to Player 1, Ball 2:

- The Player Unit and Coin Unit need to be moving properly and all the spider finger connections have to be made. As far as stepping up to the next ball is concerned, the Coin Unit is involved in a 1-3 player game, but a 4-player game bypasses the Coin Unit and goes through the Player Unit only to fire the Ball Count Unit S.U. coil.

- It sounds like your Player Unit S.U. coil is firing since you're able to go through Players 1-4.

- In order for your machine to go back to Player 1, the Player Reset Relay has to fire, so the EOS switch on the Ball Count Unit S.U. coil needs to work. There is also a M/B switch on the Player Reset relay that has to switch.

- After the Player Reset Relay fires, the Player Unit Reset coil should fire - that takes the Player Unit back to Player 1 from wherever it is.