Thought I would share this with you from my own fix of a non-working numberplate light when the bulb is known to be good. I had the check numplate light dash message and my right side light didn't work.
This was performed on a 2004 X5 facelift model which has the boot release handle and 2 numberplate lights in a removable strip assembly on the bottom edge of the tailgate.
I have no photos as it was a 4 hand job so i will try to do a step by step guide to fixing it.
This is a common problem on numerous models and a stealer will charge around £100 for a replacement assembly, the problem I think lies within the assembly conductor strip construction allowing water ingress to potentially corrode parts of the strip and thus restrict continuity the bulb holders.
Removing the strip is simply 4 torx bolts.
Be gentle upon removal as it has a small connector plug attached, release this plug to release the assembly.
My wiring configuration is as follows: Left Light Trigger - Black/Grey
Tailgate Release Button - Yellow/Grey
Right Light Trigger - Brown/Grey
Brown - Ground
The strip/wiring configuration in the bar is as follows: Left Bulb Holder - Left Side Ground
Left Bulb Holder - Right Side Trigger/12V supply
Right Side Holder - Left Side Trigger/12V Supply
Right Side Holder - Right Side Ground
After checking continuity and 12V supply across both holders it became apparent that I had good earth on the right holder (non-working side) but no trigger /12V supply when the lights where switched on. I then checked the plug that supplies the assembly, which was all good.
My idea and actual fix was to drill a small hole next to the left side of the bulb holder (on the non-working side) as this was supposed to be the !2V supply side.
I then fed some suitable wire thru' the hole and carefully soldered it to the left side of the bulb holder. I then put the bulb back in and put the cover back on as the work to the holder was now complete.
I now focused my attention to the back of the assembly to tape down the wire in a suitable route to avoid the fixing holes and make it's way towards the plug connector socket.
This is where it became fun as I needed 4 hands. 1 to hold the boot lid in a good position, 1 to hold the light bar, and the other 2 to scotch lock the wire I had just ran from the holder to the Brown/Grey going away from the connector plug.
Tried the lights and well nothing had changed.
I checked my scotch lock and it hadn't seated properly (fiddly buggers they are) so I tried it again and Bingo, I now have 2 fully working number plate lights no message on the dash and no potential issues at MOT time.
I hope this helps some of you out.