Trailer lights can be a tedious pain --- I've found for me the best way to deal with them is to get a battery, set it near the tongue, and then individually (with some small pieces of wire) test every combination of power to the different circuits (?) of the trailer. When I do it that way it helps me figure out if it is a trailer wiring problem or a truck/trailer connection problem. After I figure out what is going on with the trailer wiring I can them test the connector at the truck with a test light or meter.
It's got to be "at one end or the other" -- the trailer wiring or the connector at the truck. There are too many variables if you try to figure it out all at once.
Sometimes you'll find that the truck connector is corroded "in" one of the holes --- that has happened to me more than once -- you can clean them with electrical contact cleaner and either a very small wire brush (like you use to clean a gun) or some rolled up (with the rough side out) emery paper.
And sometimes the connectors just get old and corroded enough that it is almost easier to just replace them. But I save that as the last resort.
Good luck with it
Jeff



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