On my 2001, and I assume all of them, there are 24 LEDs wired in 6 parallel groups of 4. If any one LED fails, it will take out the group of 4, but other groups will stay lit. 12V powers the whole strip, and with that supplied (I used a cordless tool 12V battery for bench testing and repair), about 9.25V drops across each group of 4.
Not having spare LEDs, my solution was to first swap one of the end (#1 or #24, say #24 for this example) LEDs in place of the dead one. Doing only that would kill the entire #21-#24 cluster, which is an improvement, but still noticeable.
So I then did some calcs to find the right sized resistor to solder in place of the missing LED. This way, all lights are evenly illuminated, and missing a single LED on the very end of the strip is not noticeable. It would have been better if I had a spare LED of the right voltage and intensity, but I was glad to fix it without a trip to the store or waiting for a part.
BTW, before making this permanent fix, I was able to fix it temporarily (thinking it was permanent) just by reflowing the solder on the near-dead LED. Discussed in:
https://xoutpost.com/bmw-sav-forums/...ml#post1060746