If the problem stays on the left side the problem is not the bulb. It could be the bulb holder or the wiring or the LCM. If the problem moves it's the bulb - go to the stealer and get a genuwine BMW bulb. Try swapping the bulb holders. It may not be possible as the electrical connectors may be keyed for left and right. Try it anyway. My display is stuck showing --:-- and my BC button does not work. Also the two buttons on the cluster are not working. I have taken it apart and they are not broken like the common issue with the stalks. This leads me to believe that the issue lies with the cluster. (Speedometer is also not working but this is probably a separate issue) The internals are actually quite simple. The LCM really just consists of some power transistors (covered by a heatsink) and a micro-controller. The micro-controller contains both RAM and a custom ROM program preset for the car configuration; the controller can directly drive the outputs and monitor the check inputs.
I have a 2001 e46 330ci 170kw. After disconnecting the battery and welding(the welder working clamp was on the exhaust pipe not the body) the muffler the IC is half working i guess. Speedometer is not working, fuel consumption not working, red battery illuminated, red oil illuminated, yellow dsc abs and brake light illuminated, washer fluid low
After checking both side, the one that worked was showing current flow through a multimeter whereas the left side marker was showing no current flow. So this means we have one side wiring not working. Also on actual plug (the one that attaches to the side marker, I could see some sections of the plastic burnt)

2). The LEDs Are Dead. Your BMW uses LEDs to illuminate the letters next to the gear. Unfortunately, those LEDs can fail because of old age, factory defects, poor handling, surges, and short circuits. Once they stop working, the gear selector letters won’t light up as usual. 3).

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bmw e46 indicators not working