Okay, so I'm lazy. But, my neighbor has a Z3, so comparisons are bound to follow.

This is pretty odd. Apparently when your blinker is about to fail, it gives you a warning sign by a) showing a red low beam icon amongst the warning lights, b) blinking the side that's about to fail really fast, and c) flashing your headlights when it senses a problem (disturbing the car in front of you to say the least).

I'm off to Stevens Creek BMW for spare parts tomorrow. It seems simple enough to fix, but I'm far from being a handyman. More boring details to follow.