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.