Your game has a lock relay. This relay is essentially wired directly to the coil power output of the transformer. Whenever the power to the transformer is on, this relay will be pulled in and will stay energized all the time. The only exception to this is when the delay relay is activated, but that should never happen under normal home usage since the delay relay is an anti-cheat device.
On the lock relay, there is a switch that is normally closed when the relay is off, and this switch opens when the relay is energized. This switch is wired directly to the trip coil of the game over relay. When you first turn on the game, the lock relay will immediately pull in. However, before the lock relay fully energizes, the closed switch on the lock relay should also cause the game over trip coil to fire before the switch points open. The timing of this is somewhat critical - the NC switch on the lock relay needs to reliably open when the lock relay is fully energized, but it needs to stay closed long enough on game power-up to allow the game over trip coil to fire.
When a machine won't go into game over mode on power up, it's almost always because either the NC switch on the lock relay is opening too early, or the game over relay is mechanically sticking in a way that is preventing the very short pulse on the game over trip coil from actually tripping the relay. So you'll want to clean and adjust the NC switch on the lock relay, and also confirm that the mechanical latch/trip action of the game over relay is working smoothly.
- TimMe