I’ll back up Frank’s suggestion. Water intrusion into the taillight assembly can cause advanced corrosion, or a pinched wire over time may have worn and found a nearby ground. It’s been too many years, but seems I had a similar issue decades ago, and attending to one of the taillight assemblies, wires, or lamp(s) resolved it. Keeping water out and/or providing condensation a clean route out are advisable. As Eric notes, the trailer outlet wires also often are the problem.
Joel