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Is this a trailer or motorhome? Not clear from your question here.
Probably in the connection behind the taillight assy. That would be the most likely. IF it were just on the boat that would usually be in the taillight converter on the motorhome or in the plug or wiring on the boat. Both sides come back to one or the other lights (usually the left side) and then the right side goes over from there. That would be the first place to look and using a 12 VDC test light would speed this up. Hope that proves helpful here. Please get back to me if we need to dig deeper into this as all follow ups are included in our fee.
A loose connection could do that as the voltage changes when the lights are on. Start there and let me know if we need to go further.
Just checking back in to see if you were able to resolve this issue with the help I provided or do you still need some additional input from me here?