I had the exact same issue when I installed the TruckLites. I did everything I could to track down/correct the problem, including the harness kit from Susquehanna Motorsports, which did nothing for me. While the harness is great, and I do suggest it when upgrading your headlights, it won't fix the issue you're having (assuming itís the same one I have). The reason it won't fix it, at least in my case, is that you are using the original headlight circuit to close the relay that comes with the harness, but when the voltage on that circuit drops (0.2V in my case), it isn't enough to keep the relay closed (I seem to recall reading that 5-7V was required), so you end up with the same problem whether using the harness or not.
The issue, as far as I can tell, is with the TIPM (Totally Integrated Power Module). If you search the forum, or Google or whatever, youíll get a ton of results where the TIPM causes quite a few problems on numerous systems. I cannot guarantee that this is what is wrong with yours, but it would be my first guess.
FYI Ė I havenít had any problems with mine other that the headlights, so I just decided to use the parking light to trigger the relay for my headlights, that way I can still use the factory switch.
If the above makes no sense whatsoever, itís because I have the flu and have no idea how many meds Iím on at the momentÖ If I need to clarify anything, just ask, Iíll do so when my head is no longer in the clouds.