OK, I checked my machine in novelty mode. When you start a new game, The AX relay latches. The score motor runs, and both the lightbox advance unit and the ball count unit reset coils start pulsing. This pulsing continues until both units are reset (stepped down) all the way to their zero positions.
There is a switch stack on the back side of the lightbox advance unit. When the unit is reset to the zero position, a post on the toothed gear pushes on this switch stack. The switch closest to the post is closed when the post pushes against it, completing the circuit to release the AX relay.
The double-wiper on the ball count unit disc bridges the rivets located at the zero position of the unit. These two rivets, when bridged, also complete the circuit to release the AX relay.
So, both the switch on the lightbox advance unit and the rivets on the ball count unit must be closed in order for the AX relay to release.