Issue only when wet. It's very likely a short. If only when driving, and not just sitting out in wet weather. Likely, under carriage wiring. I'd start by disconnect (unplug) each wire housing block, under rear area. We've one bunch comes out from LH rear 1/4 and another near exhaust tail pipe. Look for one grimy inside. If you find one. Clean with plastic safe electrical parts cleaner. Then add dielectric grease, on the seal seen in housing.
Look close also at wire near exhaust. I've seen one with hole resonator. It metaled the whole bunch of wire housing blocks, just above resonator/tail pipe.
I've also seen were rodents have chew wire sheathing and wires. That when wet, complete a circuit. So look closely at all wire sheathing.
One way you may be able to isolate. Spray water, in only one area at a time.