Originally Posted by Pstone
...should the connector get so hot that it melts the insulation on the connector and what would cause it to do that?
No, it should not do that.
Heat in an electrical circuit comes from electricity running through a resistance. The connector doesn't QUITE conduct electricity as easily as wire does (that is, it provides some resistance) so it gets hot first. Think 'doorway' as a crowd is trying to push through it.
Normally the amount of electricity running through the connector is waaaay below what would cause it to heat up like that, so that means that it is getting waaaay too much electrical 'traffic' that it is designed for. That's likely (well, almost certainly) because there's a short circuit at the other end.
A short circuit is where the wires that supply electricity to the motor (or light, etc.) at the other end are touching each other or the body of the bus. That way the electricity has a shorter way to get back to the battery/alternator. So much electricity goes through the wires that one can easily start a fire or melt the insulation off the wires from one end to the other.
Fuses are SUPPOSED to melt before the wires do. Most of the time they do (though I lost the wiring harness on a car once when it didn't). In your case, finding melted fuses should have prompted a bit more looking for rubbed wires or the like before firing it up. But - hopefully you shut things down before melting the insulation.
For testing, I would suggest buying a cheap ohmmeter or multimeter. Harbor Freight gives 'em away with coupons, or sells 'em for eight bucks or so. Use the 100k resistance setting, and look at the dial. It will show infinite resistance. Touch the test leads together and you'll see the resistance drop to zero (indicating a short). LABEL and then disconnect everything at the lift, and put electrical tape over any exposed wires that you disconnected. Pull those fuses so those wires are disconnected from anything at the front of the bus. At the fuse end, find the wires (or the connector for the fuse) and use your meter to check the resistance between each wire and ground (the unpainted metal of the bus body). Then check resistance between each wire and the next. If all is well, you OUGHT to have infinite resistance everywhere, showing that each wire is on it's own and not electrically connected to any other wires or the body of the bus.
If you see low resistance between any two wires, you may have burnt the insulation along the line somewhere. Might need to replace the wire, front to back. If you see low resistance between a wire and ground, look for places the wire might have worn against the body and damaged the insulation. If you find a place where the insulation is rubbed bare, use electrical tape to insulate it and see if you can reroute the wire or put some sort of cushion there to prevent the same thing from happening again.
If all of the wires show infinite resistance between each other and between the wire and ground, I would fire up the bus and see if things got hot. If the don't, the problem was in the lift motor or a switch or something at the far end - after where you disconnected things. Can't help you much there.
Hope this helps.
Disclaimer: I read a lot and have done some electrical work in my time. And I taught high school science. But this is a tinkerer giving an opinion, rather than an expert electrician talkin'.