I traced it to the 36V solenoid which was stuck in the open state. I put 36V on the control terminals and hear it clicking but my multimeter shows that the contact never closes. The solenoid lasted 24 years so I guess that's good enough and I threw it away.

Two days ago I went to the golf cart store and bought a new 36V solenoid. I tested the solenoid before putting it in and it tested good.
I installed it and drove the cart around but after a while I realized I didn't hear the solenoid clicking sound when I push the pedal. I checked with my multimeter and it showed that the solenoid was stuck in the closed state! What would cause the solenoid to stick in the closed state??(36V was not on the control terminals).
After letting the cart cool down for a while, I can turn it back on and push the pedal and then I hear the solenoid click and it starts working again but after 5-10 minutes of driving, the solenoid gets stuck in the closed state again. Let cart cool down, repeat. 

What could cause my solenoid to get stuck closed? Or should I assume it is defective and try to return it?

Also I noticed that I can put either +36V or -36V on the control terminals and it closes the contact, is that how it is supposed to work, the polarity doesn't matter?