Sounds like yours is definitely an alternator related issue with the dimming instrument panel light. Mine was a contaminated wiring harness connector at the transmission. The factory had not packed any sealing grease in the harness plug. After a trip through the car wash one day, the transmission went into fail-safe. When it dried out about an hour later, it was okay. Before tracing the problem, it happened again after a heavy rainstorm 400 miles from home, only then I couldn't get the lever out of neutral for two days! Once back home, the mechanic spent an hour and a half cleaning connector pins - it was full of dirt.

2002 X5 3.0 241,000 miles
2004 325i 107,000 miles