Red Hot Resistor Coil

[frankcneal]

I have an older E-Z-Go electric three wheeler that recently has given me some problems. There are two sets of numbers on the data plate riveted to the inside of the front cowling, 79418 and 187645. I know it is older than 1998 because that is when I bought it, very used and abused, but runable for the deer camp, kids fun etc.
Recently the golf cart is experiencing electrical problems and runs the batteries down very rapidly. If I put the unit in forward or reverse it runs OK when the accelerator pedal is depressed, but if I do not press the accelerator pedal the resistive coil gets red hot very quickly. If the Forward/Reverse switch is in the neutral position the resister coil cools down. I think I recall a clicking noise when I depressed the accelerator in the past, prior to this problem, but not sure.
If the solenoid were defective (shorted out internally) would this cause my problem?
Any advice, troubleshooting techniques, or other help would be greatly appreciated as deer season starts in 16 days