I had a similar problem with my side maker light and it was never resolved I think it was an internal fault in the LCM.

You get voltage but no current usually means a bad connection somewhere. If you can find the pinout for that lamp, measure at LCM to determine if it's wiring. You need to load the circuit so use the likes of an old timey circuit probe with lamp in the body of the screwdriver looking probe.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)