[Destroyer]

Everyone has their own solution to the problem of corrosion on the boats wiring. I usually solder all my connections, then shrink wrap them. Lately I've been using the wire connectors from Harbor Freight that as they shrink they seal at the same time. They seem to be working good. I'll let you know how good (or bad) in a couple of years.

Now, back to the problem. I'll try and make this simple. Skunk is correct, the nuts spin down onto the pigtail wire coming out of the light that usually has an eye connector attached to it. The eye connector usually is fitted over and around one of the two bolts that come from the light and are set into the plastic on the back of the traller light. When you fit the light to the trailer mount you push the two bolts through the two holes in the mount, then you slide the wire over one of the bolts. When the nut makes contact with the wire it squeezes it between the nut and the metal of the trailer light mount and makes an electrical connection to the metal of the trailer (ground) Since the lights are new, that means the bolt and the nut are new and don't have any rust or corrosion on them. So either the hole or the area around the bolthole is rusted and preventing a good ground (doubtful since the nut usually scrapes away enough rust to make a good ground) or the light is faulty or there is a problem with the wires somewhere. In all cases, since the light on the other side works great, a simple switching of the right and left lights will be enough to determine if the light itself is faulty or if the wiring is faulty.
If the light that wasn't working on the one side suddenly starts working on the other side, you know the light fixture is ok and you have a wiring problem. Quick and simple...the whole test should take no more than 10 minutes, 5 if you're fast. Simply a process of elimination. Once you determine if the light is good or bad you can work from there, but finding out if the light is ok is the first step.

or

You can take a spare 12 volt battery, or even the leads from a battery charger, and connect the ground wire to the ground of the battery, and then touch the other wires to the positive terminal of the battery to see if the light will light properly. Again, if it does you know your fixture is good and your wiring is bad. If it doesn't then you know your light fixture is bad.