Here's a site with lots of wiring info.
http://www.jeepkj.com/forums/viewtopic.php?t=1691
Now he refers to the "chosen few". That's peolpe who don't have the evic. The cable for the evic also has more wires in it including one with 12v on it to the rear where the mopar towing harness with the RELAYS WRAPPED IN A BUNDLE are. Without 12v in the rear the relays for the trailer won't have power. If you need the second cable you may want to stray from the instructions a bit. There are 2 wires that need attatched in the front of the vehicle. One switches the trailer 12 volts on and off. They have you hooking it into the 12v outlet on the dash. The problem is it's always on
There's a fuse by the driver's door panel that has a fuse listed for that. I hooked onto the rear of it and now it's "switched 
The second wire is to take 12volts to the rear from the battery. They have you putting a inline fuse then hook to the positive terminal of the battery. The situation here is there's already a fuse in position 10 for "trailer" on the power distribution box by the battery with a wire that goes into the jeep. It's the same color as the wire they want you to put on the battery. If your adventuress dig it out under the dash. Pin 54 on the big connector if I remember correctly.
Are you sure your kj is US spec because the export ones vary slightly in wiring?
Good luck
Joe