JK's are Unique beasts. Technically you shouldn't wire anything into them without using an "approved" accessory wiring "whatchamacallit". Chrysler started using solid state switching with the ignition switches in them ( that's as bright as the keyless key and pushbutton start switch). Some have no problems hooking accessories up in a conventional manner, others have all kinds of headaches. So anything you have hooked up that wasn't original equipment and isn't directly wired to the battery, should be temporarily disconnected before trying to chase this issue down. If it goes away its the JKcurse, if not, then you know what isn't causing you a problem right off. A couple pointers: anything that goes through the fire wall can be a problem so it should have an inline fuse on the power side of the firewall, in case of a short. if it comes from the battery through the wall to a switch and back out the wall consider two fuses for safety sake (Ive seen people rewire things and forget to add a switch, for example disconnect the power lead going to the switch from the battery, and replace it with one from the hot side of the fuse block, and next unless it is blatantly obvious, LABEL all the leads and wire tie them together for as far as you can, incase you have to do future trouble shooting. Electrical issues can be the biggest head ache there is in automotive work, and even worse in 4 bys that are used off road due to vibrations messing things up. One of the hardest parts is lending a hand online because we cant see it personally