If you don't have one, a trailer light tester is a handy tool for under $15. It may help you find which wire(s) are having issues, which could indicate where the water you suspect might be.
If it was bothering my that much, I'd start with a good spray of circuit cleaner several times. If that didn't work, then see if the thing is able to be disassembled easily. If it is, disassemble and clean out. If not, maybe look into replacement. No idea the price of that connector.
As others have said, maybe there's another connector upstream of it that could be the culprit as well.
Good luck. These kinds of problems can be perturbing.