I had the same issue.

There is a clear plastic lining inside the taillight housing. Mine had come loose inside the housing and was leaning on the bulb. I had several burn out, crack and explode before I figured out what was happening. The last time, the bulb actually melted into the plastic so far that it wouldn't come out.

I got the bulb out in pieces, and the lining was completely loose at this point and rattling around inside. I then used large needle nose pliers to grab, twist and break the inner plastic lining, until the pieces were small enough to come out through the socket hole. I put a new bulb in and haven't had an issue since. The light looks no different than the right housing which still has the lining intact both with the brakes lit and without.

If there is a way to get the housing apart to remove the inner piece please don't make me feel like a complete moron when you tell me.

Who knows, this may be the same issue as the op's. Worth looking at. I looked at LEDs but wanted to spend the money on different things.

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2005 CRD 75,000 miles
Various mods, I just fix it till it breaks.
The rest of the fleet:
85 F250 6.9 Diesel 250,000 miles
82 Mercedes 240D 330,000 miles
81 Mercedes 240D 285,000 miles
My kids think gas is only for lawn equipment!