The Royal Flush manual calls for a ratchet and cam assembly part number A-15659.
The parts catalog says that that assembly has a C-15221 cam on the left and a C-15658 cam on the right.
Watching the cams work their switches have a repeating pattern of 5 steps:
- both switches open
- right side closed
- right side closed
- right side closed
- both sides closed
which makes sense if you think about how the bonus is counted.
/Mark