On this era of Gottlieb, Game Over is mostly controlled by the Match Relay. If the Match Relay doesn't activate, then it won't reach game over.
Specific to Cross Town though, Game Over ('X') is fed by two switches on the Match Relay ('O'), and switches at score motor 1A and 2C. If 'O' is activating, but 'X' is not, then those are the four places to check.
But if 'O' isn't activating, then need to look into that first. On Cross Town, 'O' is fed by either the 4th and 5th ball trough switches (5-ball play), or the 2nd and 3rd ball trough switches (3-ball play), plus a normally closed 'On Ball Release' switch and a switch at score motor 1C.
The switch at score motor 1C is common to lots of other things, so that's likely working if the rest of the game is working. The 'On Ball Release' switch is often a culprit, as it's in the switch stack there at the ball trough gate, and that switch stack frequently gets bent. The ball trough switches can oxidize and not make good contact too though.
However, since the ball trough gate isn't de-energizing, the Ball Release coil is activated via a switch on the 'Z' (Reset) relay, and then held active via a lock-in switch on the Ball Release switch stack and a normally closed switch on the 10pt relay ('N'). The ball trough gate will stay open and let you keep playing ball 1 until 10 points are scored. Then when the 'N' relay pulls in, that switch is supposed to open and deactivate the Ball Release coil, closing the gate.
So those might be some places to look.