pedantically, a stepper unit resets to position 0 then steps up from there. You just have the less common case where a stepper unit is usually sitting at its top step rather than it's 0/reset position. Top = where there's a missing tooth on the ratchet so the thing can't physically step more.
the switch on the left operated by the white plastic peg is the "open at 0" switch. It just disconnects the reset coil when the unit has reset.
the other switches are all operated by the metal peg and on this unit are all closed until the unit is at the top step.
whether the unit steps up 9 or 10 times from reset you'll need to check, but it doesn't matter much. As long as the three switches don't open until the unit steps to the top step, that's what ya care about.
the three switches not necessarily in order on the stack are:
1] white/green to somethingmaybe mostly green - turns on the super J.P. light
2] no idea on the wire colors, but one wire goes to the step-up coil on the super jackpot unit so the step-up coil doesn't fire when the unit is at the top step
3] yellow and green/white. In circuit to keep the super J.P. relay powered until you've had your ten spins.
note since the 1-10 numbers count down, unit reset = lamp 10 lit.
attached is the schem piece for the circuit. It's possible the open-at-top switch is ok and switch in the right branch on the super J.P. relay is the problem IF the regular J.P relay normally unpowers when the handle release is tripped. Might as well check that switch first and if no luck, I'd either jumper closed the [3] switch above to see if the super J.P. relay stays powered like it should or bung a voltmeter on the circuit to see where the issue is.