Is this for an R80ST? Well, as I recall, you have to be able to pull the holder in order to put in the new bulb, which sticks up inside the speedo pod. I would imagine that it turns, likely turns say 1/4 the way on direction and then pulls out. Does yours look like it might turn to the left or the right? It can't pull straight out otherwise it wouldn't stay in place. So, I would think that it has to turn then pull out. It's #4 on this diagram:
https://www.realoem.com/bmw/enUS/sho...29#62131243519
It may be possible to buy a new one...it doesn't appear to cost that much.