Since it is happening at start up it easily could be a single score reel zero switch. Look at the very upper left part of the schematic where the reset relay is. The reset relay is energized during start up, and it is held energized by its own switch which is a lock-in switch and also in series with NC score motor switch 8C. When the score motor rotates around and gets to position 8 then that 8C switch will open, cutting off the lock-in circuit and denergizing the reset relay UNLESS any score reel zero switch is still closed. You can see this in a parallel circuit to the lock-in circuit labeled "(16) score drum units zero".
There are 4 players each with 4 score reels so there are 16 total zero switches. The schematic has a shortcut notation (to save space) by showing just that one open switch, if it were truly accurate it would show 16 different zero switches all lined up in parallel. All 16 have be open to cut that circuit off so the reset relay will deenergize when score motor switch 8C opens and then this will stop giving the score motor a signal to go.
Those switches are open when the score reel is in the zero position and closed otherwise. So make sure all 16 of those are set up right. If just one is staying closed at zero you have this problem.