HotRod is right. AS an old (and I do mean old) electronics technician, I can verify that where there is HEAT, there is RESISTANCE. The bottom connector, as I recall, is the one that goes from the solenoid to the resistor group, so it is important that is a VERY good connection. Here is the schematic that I use in a book I wrote for the model I think you have.
The stud is certainly important. It connects three wires: the wire to the resistor group, the wire that goes to the solenoid, and the flexible braided wire that goes to the wiper. It doesn’t get much more important than that. I don’t know how your “homemade” stud looks, but as long as it connects these wires together without any resistance it should do the job. If one of the contacts that the wiper touches gets hot (usually because of a bad connection the back side), it usually melts its way down in the plastic so that it does not make proper contact with the wiper anymore, and then you’ve got a real problem. But the stud I think you are talking about is just a contact point for those three wires and should be ok as long as it keeps them connected together without resistance.
Yes that stud connects those 3 together. The only place I see that got hot was the wiper side of the stud. The contacts are all clean etc and the wiper seems to glide perpendicular with the pads. I did put it on jack stands and I that stud got hot. Would low voltage be an issue?
I just hate it when everything is perfect but it still doesn't work (just kidding). It looks like you are just going to have to let it get hot again and look a little closer. Maybe someone else has a better idea, but I have never experienced any unusual heat problems at that connection on that model. I've owned several of them through the years. Of course, there will be some warming of all of the wires on the high energy side (motor, F/R switch, v-glide, and the wires between them), but there shouldn't be anything excessive. The only thing that is meant to get HOT are the resistors (that's their job).
If you had a bad battery, there would be lots of other symptoms, like chugging under a load, inability to operate at all, or something. You definitely need to put a meter on the battery pack and make sure that it is somewhat normal (37.9 or so without a load and not dropping more than a volt or so when moving the cart), but if that is ok, and you still have problems with that contact overheating, there has to be something wrong right there. Does the motor spin the wheels when on the jack stands? If, for some reason the motor won’t spin, that would change everything. A stalled DC motor with voltage applied will draw excessive current and cause all kinds of things to overheat. The cart kind of internally hemorrhages trying to get that motor to spin.