I had the same issue with my 96. This is what I have been told. The fan cluster plug on the back of the climate control panel on 96 and prior XJ's has a tendency to overheat and melt. A very bad design. A mechanic friend told me that when the fan is run on the highest setting the wiring can't handle the electrical load and eventually fails. Sometimes only the highest setting is affected. Pull your control module out and look at the plug. It is right behind the fan speed control switch. Check to see if it is melted. If it is not then the problem may be elsewhere. I replaced my plug and everything was ok after. I had to splice it in.

When I go to the junk yard I check the plugs so I can pull it if it is in good shape to have as a spare. I looked at a lot of them and found most have had some kind of heat damage so when I find a good one I get it.

 

Sorey to reopen an old post but I found find much more about this issue. I’m having the same problem and my wires are melted and corroded. How’d u splice yours in?

 

Here is the only real solution. You need to install a separate relay for each fan speed on pre 97, due to poor factory design.

By doing this only a small current needs to flow through all the switches, wires and resistors

failure to do so is inviting failure into your life

I mounted mine behind the kick panel, but did not relay out the highest speed, as it is not wired through the resistor block). I avoid using highest speed

However a guy saw my writeup, and added to it with his "all 4 speeds" relay bypass, this writeup is in the archives here, my username "96 headlight relay" this sub forum

an aging fan pulls big current on startup, there is miles of wires, the resistor pack wiring is almost aways burned. The ignition switch is very vulnerable. There is a 30A fuse

 

The blower control switch and plug on my 96 melted. Splicing in the new plug is a PITA. There isnt much extra wire to pull out so its easy to work with so only cut off as much wire as you have to for the new plug.

On second thought, after reading again and seeing your wires are melted and corroded, you may have to just take apart the dash more than you'd like to, to be able to get to the good part of the wire that isnt melted or corroded. Or you could figure out where the other end of the wire goes and attach new wire to that end and pull the old wire out through the A/C control panel hole, dragging the new wire with it. I'd go up in wire size if I were to do that to handle more current.