A relay that is operated by the reversing switch to power the motor. A microswitch at the stent of travel to break the circuit and stop the motor.
You'd probably need to use some multi contact relays and do some cross wiring to control the stop/start and forward/reverse for dropping them and raiding them.
You could use an MCU to do it too. Probably just a couple of servos or stepper motors and program the exent of travel in software. You'd probably only need a couple of pins so maybe something like an ATTiny would work.