I think this is the relevant circuit:
Contest Roto Target (resized).jpg
Since things seem to work when you get 50 points, that helps simplify the circuit quite a bit. The 50 point circuit is in red and is used when the Roto Target is in position 5. In this case, the Score Motor 1A switch closes 5 times as the Score Motor turns through one cycle. Each time the Score Motor 1A switch closes it sends a pulse through the circuit to fire the M/10 point relay. Since the points score in this case let's assume for now that the F and L relay switches and the Score Motor 1A switch are working as they're supposed to.
The way this circuit works for Roto Target positions 4-2 is that each position adds another normally closed Score Motor switch to the circuit to block one of the 5 pulses from Score Motor switch 1A. So when the Roto Target is in position 4 for example, the Score Motor 1D switch opens to block one of the 5 pulses from the Score Motor 1A switch, and allows the other 4 pulses to pass through to the M/10 point relay. Position 3 adds the Score Motor 2C switch to the circuit which would block a 2nd pulse, allowing only three pulses to reach the M/10 point relay. And so on.
I'm not familiar with this game but is seems possible that there is a Roto Target position 1 (not shown) that includes all four of the normally closed Score Motor switches in the circuit which together block 4 of the 5 pulses, allowing only 1 to reach the M/10 point relay.
Given that you can only score in Roto Target position 5, I'd first examine the Score Motor 1D switch to see if it's stuck open. If it does not close, it would effectively block all pulses to the M/10 point relay unless the Roto Unit is in position 5.
/Mark