I've discovered what the problem was. There's a known issue with a clear plastic surround inside the tail light housing being affected by heat over time. Eventually it breaks away and touches the bulb, creating a hotspot that quickly burns it out. I took the unit right off the Jeep and gave it a shake and what do you know, that's what had happened to mine. It's a hefty chunk of plastic rattling around inside the tail light, but it's invisible from the outside.
Officially the only fix is to replace the entire tail light housing, but unofficially you can get some needlenose pliers in there to break up the plastic and pull it out (it's toughened, so it was a real PITA). Even though the plastic is supposedly some kind of lens, there's no appreciable difference to the brightness of the light compared to the passenger side once you've pulled it out. Hopefully my problem has now gone away.