[Fairtax4me]

That wire provides the negative path for the solenoid through the microswitch inside the V-glide.
It’s what completes the circuit for the solenoid and makes the solenoid turn on when you press the pedal. If the wire is not there, It’s possible someone removed it at some point and wired the solenoid so it only needs the key switch on to turn on.

All of the power for the motor runs through the throttle wiper arm on this setup. So if the wiper or the contact pads are damaged you will get no power to the motor.
It is common for the v-glide to fail on these because the drive system was designed for a golf course use where the cart only runs for a brief period, then stops. Continuous use or running at mid speeds for a prolonged time will eventually cause failure of the v-glide.