Sounds like corrosion or a bent tab in the area the bulb holder slides into and locks in place. Take a set of needle nose pliers and gently pull up on the contacts around where the bulb holder goes and bend them up just a little, especially in the little locking notched areas.

Had the same exact problem but had to figure out first if it was the bulb or a bad contact . Real easy fix after removing the tailight housing . It turned out to be both a bad bulb and the socket contact .

I am sure socket contact created this crazy warning. I had the same problem and fixed it months ago.

I had this issue a couple years ago. Brake light was out, spent get a ton of time trying unsuccessfully to get a new bulb in there. Turned out that the plastic housing had actually deformed making it impossible to fit a bulb. So I ended up having both the light housings replaced. It was somewhat of an expensive fix, maybe around $500 total, but I have not had any issues since then.

Another corrosion issue here!I had the surface and bulb contact area badly corroded,but only on the left rear light!It was so bad that I could hardly remove the stop light!
Had to sand down the whole area,apply contact spray and so far so good.
It seems that the lights rubber sealant was defective and let water in that area...

Thanks for this post, I've been dealing with this recurring issue and this is a far more agreeable solution to taking it to BMW service!