Vintage Car & Truck Parts

I have a brand new car hauler tailer with LED lights. I have a GMC Yukon with the round (7 pin I think) plug. I noticed when I got home that the right rear two tail lights are still dimmly on. All other lights are off. This is with my car off, parked, and sitting in my driveway. I had to unplug the trailer from the Yukon to get the right rear red taillights to go off.

I have another trailer with regular lights. I have never seen the right rear dimly on when the car is off.

I have to figure it's in the car. For some reason one power wire must still be hot when the car is off or have a tad bit of juice to it. Any ideas? Is there a tester I should buy?

Thanks,
Steve