1998 Chevrolet Silverado Tail Lights

This is typical of a broken ground wire on one of the sockets. You can verify that by observing the symptoms will change when you remove what appears to be a properly-working bulb on the other side.

If it worked before, it didn't suddenly start causing a problem, but what I'd look for first is if any wires were attached with Scotch-Lok connectors. Those don't seal out moisture, and will lead to corroded wires.

If your adapter is simply plugged in to existing plugs, those do have rubber seals to keep water out, but I'd still pop them apart to look for corroded terminals.

If they're related to that adapter or are near the rear of the box, you may have found the cause of the problem. If any wires were recently cut, you can splice and solder them back together. If they corroded apart, water will have gotten into the insulation and the wires will be dark brown. You have to cut the ends back until you find nice shiny copper wire to solder to. Solder won't adhere to the dark stuff. Splice in a piece of new wire if you have to, then seal all the solder joints with heat-shrink tubing. The best stuff has hot-melt glue inside to really seal out moisture.