99 wrangler fan work only on high what the most likely part that need replaced

The winding in the motor may have a short. drawing too much current when trying to run on a lower speed.

May help - fuses supply power but also needed is earth return to battery. This is usually black wires running from device to the car metal. To diagnose you need a multimeter. Check body of cigar lighter is connected to the chasis with meter on ohms. (continuity test) good is zero ohms. If earth problem, check under dash to ensure all earth wires connect to metal chassis. Then with ignition on, check centre pin at back inside cigar lighter has 12 volts to side.
If not then check fuse has 12 volt to it, Now you can get to the fan, repeat all the tests on fan. Best wishes, its tedious work.

This is 100% the Blower (Fan) Motor Resistor located near the Blower Motor.
This is a very common problem with Chyrsler, Dodge, Jeep and Plymouth. The key symptom is the Fan only working on High.
This is very easy to access and replace.

Let me know if this helped....

Yes I would go with the switch, BUT, does it have a resistor bank? That is, how does it reduce the speed? Many systems use resistors to lower the speed. Burnt or bad connections can cause this as well.
You can test the blower motor by connecting direct power from a source like the cigarette lighter if you are handy.
Most of the time the lower speeds konk out but the high speed continues to work this is the resistor bank that goes out.

Very common problem... it is usually because the resistors are shot... the resistor block is kind of tricky to get out but, its a cheap fix... it is located behind the glove box. it is also common for the switch/connection to be corroded or cracked... if you have any difficulty i would be happy to add more info about removal/install...

Well if those two pins look melted, chances are there not making a good contact connection with the other side of the connector. Make sure your ground wires are clean and tight, and you should replace those melted pins. You really cant go much further until you resolve that issue.

check the idle speed sensor also the map sensor

Mine only works on the highest setting, did you figure this out yet?

Check it with a test light or Multimeter for power to blower motor first, with switch on high. If no power to motor, problem is elsewhere. Here's a link that will help you. Click on the pictures to expand.

http://www.autozone.com/shopping/repairGuide.htm?pageId=0900c1528008ac7f

your switch is broken, take it in and get the switch replaced.

tepfy