Funny you have this problem.
On my 94 psd, I bought those waterproof led tail lights, the exact same thing happened. (Just the tail light function, two LEDs per side)
I guess I didn't notice it when I hooked them up, but noticed at my gf's house later that night.
My trailer plug was for sure cross feeding. So I just cut it out at the time.
Between that and hooking up the front and rear side marker lights (4 total, incandescent) and hooking up the headache rack lights (one on each side, incandescent) it quit doing it.
So no help really, just my experience. I'm changing the rest to led eventually, so it may come back, but then again, 8 lights may be enough to shut it down.
Sent from my iPhone using Tapatalk