Trailer wiring and failed bulbs that don't look failed can definitely cause this but every time I've seen this tail/brake light problem on an 80 it's been caused by the failed solder joint of the ground wire on the side of the brake light socket. You can pull the bulb/socket out of the housing and play with the grounding to test pretty easily.
To test, remove the tail light that's impacted and then once you get the bulb/socket out of the housing use something to wedge the brake pedal down. I jam something between the brake pedal and the front of the driver seat bottom. Then, go to the back of the truck where the brake lights should all be on and play around with the ground wire that's on the side of the bulb socket that you removed. If pressing ground wire onto the socket turns the light on and releasing the ground wire turns it off you've found your issue. Also, this sometimes only shows up when the running lights are on (when it's a weak but not fully failed ground connection) and can take the form of the third brake light acting up when the lights are on and the brakes are pressed.
The fix the ground I've had luck with pulling that ground wire out where you can clean the end up. Stretch it out forward towards the bulb, where it's still in the socket housing, don't pull it back and out of the socket altogether. Trim the old wire/solder and strip to fresh wire and scrape/clean the side of the bulb socket where you'll solder the wire back on. Then, to make soldering it in place easier, bend the ground wire so that it holds tight to the socket's metal side with plenty of contact area and then pull the wire back until it's resting where you want to solder it in place. After that, use a decent soldering iron to heat the metal side of the socket really well and then solder the ground back on. Make sure that the solder melts when touching the socket side vs. just the wire so that you don't make a cold solder joint that just fails again. The wire is easy to heat up but the bulb socket takes more heat/time to get up to temp. If you time this just right you shouldn't melt the plastic around the socket but should get a nice clean/strong solder joint.
