My headlight switch was overheating on my XJ, so replaced the switch. Didn't help - continues to overheat, especially when the high beams are on. I went to replace the switch now for the third time, and found the wiring harness had overheated and nearly caught on fire. I replaced the wiring harness, not when the headlight switch is on, the rear wiper runs constantly, even when the switch is off, the turn signals or 4 way emergency lights won't work won't work either when the headlights are on. When you turn off the headlights, everything functions just fine. HELP

 

You have 2 problems you need to address. 1 - Why the wires were overheating. It is possible it's an errant connector, but probably something else is drawing too much power. I'd replace both headlights, check your fuse is correct and check/clean the headlight wiring in the engine compartment. As a general item, clean your grounds in the engine compartment and make sure your battery cables are clean and tight.
2 - The wiring of the connector. The issues you're describing occurred after you replaced the connector, so something is not right in what you did. I would take another look at all that stuff and make sure you have everything wired up correctly and that all the wiring is connected securely and there's nothing getting crossed up in there.

 

I would check grounds everywhere. There should be a main ground wire that goes down behind the driver kick panel on the side. I would make sure that is clean and possibly try to run another ground wire to the point to see if things get better.

 

The overheating is caused by high resistance in either the wiring or one of two connectors. There one connector at the headlight switch itself and a second located under the air filter box. The point where the wires pass through the bulkhead connector at the firewall is yet another possibility.