The issue you are experiencing sounds like an accessory problem because LED lights require so little amperage to work correctly. The ever so slight draw on your trailer wiring harness can be enough for an LED to stay lit.
You can add load resistors like # DI34ZR to your accessory, but it may not be worth the effort as you can simply unplug it when not being used. Even if you were to leave it plugged into your vehicle, the ever so slight draw would take months to drain your battery... view full answer...
Have you tried cleaning the pins of the trailer connector on your truck? Most likely you have a dirty pin that has some corrosion on it that all you'd need to do is clean with some sandpaper and that will get you going.
Check also the back of the connector for any corrosion or cut wires there and fix as needed.
I attached a help article on trailer wiring troubleshooting for you to check out as well. view full answer...
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