re: Looking for help with an issue with my boat trailer lights

Does sound like a ground issue, the ground might be corroded enough to not be able to take the extra current with the running lights on.

Use the heat-shrink butt connectors if you redo any of the connections.

I have my white grounded to the frame and each light grounded to the frame using ring terminals and self-tapping screws with the screw ends ground flush. But I did go back and prime both sides and sprayed them with undercoating to keep them sealed and protected. Every wire connection is done with heat-shrink type connectors.

I upgraded to LED, and the ones I bought had a separate ground wire. My old ones used one of the mounting bolts to make the ground to the trailer frame, or wire if you ran a separate ground.

If it helps:

White is ground
Brown is Tail Lights / Marker Lights
Green is Right Turn Signal
Yellow is Left Turn Signal