Clean both sides of the plug and apply a dab of dielectric grease to each pin on both ends, then stick with CPittman for starters. If the fuse is shot, do the obvious. If it blows again, run a test light from the correct pin on your truck plug to a ground on the truck. If that doesn't blow the fuse, the problem will be on the trailer (most likely in the end, anyway).
If it blows again . . . this may be the worst one to chase down, depending on how many running lights you have. If there's a lot of them, try to find one that doesn't work before the fuse blows. This may require a helper to check the back end. If one of them is dim or not lighting at all (even with a new good bulb), you may find it's a bad/wet fixture or a chafed wire going to it. If you can identify one bad fixture, check it out for a short (fixture and hot lead). If you can't identify it that way, you're gonna have to go one by one through the fixtures (look for continuity to ground with the bulb out--no continuity is right). If that's all good, look for a chafed wire. Depending what you have for fixtures and how many, it's hard to say which one would be eaier to check first.
If the new fuse didn't blow and you don't have lights, check the plug first, then look for a broken wire.