OK ideally you need to download the 2006 Jeep KJ service manual here....these KJs are getting old now and the Manuals are pretty much a necessity....I never travel without my Laptop in my Export 2002 CRD....the Laptop has all the relevant Manuals and I have had to make some roadside repairs a few times.
Section 8W has the Wiring Diagrams and the Index Page there you can search for Power Widows and be directed tp Page 8W-62-3 "Power Windows LHD".
Here you will see Fuse #25 10 A in the Junction Block feeding the Switch Mirror via a GY/PK wire (Grey with Pink Stripe).
It goes through connector #C301...in the Index the location of the Connectors are given...sometimes with Pictures.
You will need a Multimeter. If you do not have one then buy a cheap one....no need for fantastic accuracy!
With Ignition ON check that you have +12 volts on this Grey/Pink wire at pin #5 on the Mirror Switch with respect to ground. I have never removed the Mirror Switch...maybe somewhere in the Manual there is a description on how to do so!
Likewise check that Pin #3 "Ground" shows +12 volts with respect to Pin #5. Ground is the Black wire going to G300.
If those two pins have the correct voltages on them the Switch is a likely suspect to be faulty.
I usually tape small sewing needles to my Meter leads so as to be able to pierce the insulation to get a reading.
If the voltages are missing...you have to trace them back to look for a break somewhere. All these wires shown on this Page enter the door in a harness which may be damaged from opening/closing the Driver's Door many times!
WWDiesel is very good at breaking these diagrams down into a more basic form with pretty colors...maybe ask him nicely to help you out!
www.colorado4wheel.com/manuals/Jeep/KJ/