Why won't my fan work on high?

the switch is bad. the high position is burned out.

Yep, it's most likely the resistor pack (if that's what they technically call it). There is a little unit, probably mounted down near your blow motor, but in the airbox itself if I remember right, and it has a resistor for each speed. These often cause one fan speed to stop working while the rest works fine. From what the dealer told me with my car (I had the same exact problem), is that when these go out (which is what happened in my case), often it is because the blow motor is going bad and drawing too much amperage. You might think about replacing the motor while you're at it.

Also check all connections. They can be messed up as well. By connections, I mean the connector that goes to the blow motor, and also the resistor pack.

If the fan is working on all positions EXCEPT high, it is NOT the resistor pack.

On high, the fan is switched directly to 12V.

It sounds more like a faulty fan switch to me.... burned out HIGH contacts.

The blower motor resistor is probably open. I don't know where it is on a Jeep but, it's usually it the ductwork around the blower motor. Check a manual for location.

Check your fuse, may be blown! Don't now wat amp fuse (exmp. 5a, 10a, 15a, 20a and so on) you need (Check manual!) Walmart sells a fuse set with al amps and fuse tester. If not fuse, may be the wiring or need new heating system which may be exspensive, but try fuse first!