Connecting the trailer lights to the Jeep places incandescent bulbs in parallel with your Jeep's LED bulbs. I can see that causing weird problems. As said above replacing the TJ's incandescent bulbs with LEDs can cause several problems. That's because some Jeep lighting circuits depend on the ability of incandescent bulbs to conduct in both directions. LED bulbs only conduct in one direction. The only sure way I'm aware of to fix that is to install a bridge rectifier at each of several of the bulb locations. All the effort and expertise needed, which I have, to make the TJ's lighting circuits work properly with LED bulbs make LED bulbs not worth the effort. I know how but I still won't convert all the bulbs to LED. The benefits of LED bulbs don't outweigh their drawbacks, where a TJ is concerned, in my view.