That is the bulb for the interior door handle illumination. If you don't have a clear plastic piece sticking out behind the door handle, it doesn't need to be plugged in. I still find it silly that BMW went as far as to put the bulb in there on all cars, but not have it functional.

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2003 530i, Silver on Grey, BC Coilovers, Square 9.5" M-Parallels, Gloss Black Roof
2007 328i, Alpine White on Black, Sport/Nav/Premium
SOLD: 2006 X5 4.8is, Lemans Blue on Black