Fixed!
Here's some info, and what I did. My car is a 2001 x5, and x3's and later x5's are different in this area, but I will guess similar enough that this info will help. Based on the June 2001 manufacturing date on the unit, I'm sure this part is original, with 174k miles.
It's a plastic-welded unit, not intended for disassembly or repair, just replacement.
The LEDs run off 2.3V each, powered in clusters of 4, all soldered to a single circuit board running the full width of the assembly. Red LEDs, then a clear (white) lens, then a red outer lens.
The whole assembly is powered with 12V on the blue wire, ground on the brown wire.
Symptoms - one segment of 4 LEDs was out, the rest all worked fine. It appears that with this circuit design, when any one LED fails in any way it will take out the entire 4-LED segment.
Root cause - failed solder joint on one of the LEDs.
Solution - After checking voltages on working-vs-non-working segments and understanding the circuit, I figured it could be a bad joint and I had nothing to lose, so I just started re-flowing the solder on the joints in that part of the circuit. Luckily the very first joint I hit was the problem and it lit up. I continued to re-flow all 4 joints on that LED, for good measure.
Hardest part - disassembly of the plastic-welded light assembly. Not really hard, but I did not know how it would go, and it took some time and care to do it nicely. I used a thin Dremel cutoff tool around the entire outer seam (between the red lens and gray plastic housing). Then used a Dremel small cutting tool to cut the 4 plastic ~rivet type moldings off.
I used a 12V cordless tool (Craftsman Nextec) battery to provide 12V for testing throughout.
First step - removing the light assembly from the car: remove spoiler = open hatch, remove 2 rubber plugs near the spoiler, remove 5 Torx T30 screws (2 of them under the rubber plugs) holding it on, remove carefully. Then just 2 Philips #2 screws holding the light assembly in place, one connector with 12V/ground.
Here's a photo showing it disassembled, after the repair, with some of the tools.
