@RDW
It sounds like you likely have the same issue that I've seen/fixed on a couple of 80 series. In those cases I found that the ground wire that is soldered onto the side of the bulb socket in one or the other of the tail light housings was loose, causing a weak/intermittent ground connection. With running lights off all tail lights worked but with running lights on there was insufficient grounding back through the running light circuit so only some of the tail lighting worked. I think the 3rd brake light at least didn't work, possibly one or the other side brake lights as well.
In any case, the fix is pretty simple. From memory I did something like this:
-unmount both of the taillight housings (left and right) but leave them wired up. Should only need a phillips head screwdriver to pull 3 screws per side.
-pull the socket for the rear running/brake light bulb out of the housings but leave them wired up and the bulb in place.
-identify the ground light that is soldered onto the outside of the metal socket that the brake/running light bulb goes into. It's a smallish diameter (12/14 gauge?) black wire with the last 1/4" or so was stripped of insulation and then soldered onto the side of the metal housing.
-play around with the brake lighting with/without parking/running lights and wiggle the ground wires to see if one/both are loose and need to be re-soldered. An umbrella or something can be wedged to hold the brake pedal down while you are at the back of the truck pushing on the ground wires with a screwdriver or something.
-if the ground wire is loose on the outside of one/both sockets you can push the socket/wire out far enough to clean the socket and strip to new/clean wire in the ground wire then solder it back on well.
-When soldering you'll need a heat source large enough to warm up the metal socket side quickly otherwise you risk slowly heating the whole thing up and melting plastic/etc... Heat the socket side up until solder melts on it easily then add the wire, which will heat up quickly, to help avoid a cold solder joint. You can pre-bend the ground wire so that it basically pulls up against the socket and will stay in place for the few seconds it takes for the solder to set. I recall pulling the ground wire out too far to clean/bend it and then pulling it back to the correct spot where the bend held all of the exposed copper wire nice and flush against the side of the socket.
-etc.
Anyway, this is a pretty common issue. I should take some pictures and write a proper how-to one day, or search to see if someone else has. I learned about this fix on the forum and it saved me a lot of head-scratching for sure on mine and a friends 80 with this issue.
Good luck with it.