Thanks for the advice. I know you must be correct on the ground being the problem, but I couldn't get it resolved today.
In response to your checklist:
1). Doublechecked the bulb was correct. Center contact was touching socket contact.
2). Logically, you must be correct on the ground, though, if the tail lights work fine my brain is trying to tell me that if it's grounded enough for the tail lights and the brake light and tail lights share the same piece of metal, the brake light housing should be grounded too. Perhaps that's incorrect though. Brake light and tail light sockets are inside of the same housing, bulb sockets share internal bracket.
3). Struggling on this one a bit. I showed continuity within close proximity of the housing (bracket holding it, lower portion of bed.
In digging around under the truck (it's new to me so I don't know it's history) I found in the battery box what appears to be the remains of a chassis ground strap. It was a large, battery-cable sized wired bolted to the passenger side frame, but the other end was cut off and bent back up into the battery box.
I'm guessing that may be at least part of the culprit. Exactly where and how many ground straps are needed.
At one point I tried running a ground wire from the back of the light housing all the way back to the firewall, where another wire is grounded into the sheetmetal.
Again thank you for all the help.
On a brighter note, I was chasing another wiring problem on a different old vehicle today (ironically, also with a brake light issue). This one turned out to be a wire that had been pulled out of a connector. One down, one to go.