Parasitic Drain on the Batteries - 93 850Ci

Incidentally, member IcemanBHE is currently experiencing the same problem. He opened a topic about it on bimmerforums.com: Cluster mileage stays lit... You may want to bookmark that topic as well. Anyway, just for completeness here's my reply to IcemanBHE's thread. I put the part that may not concern you in italic, although it doesn't hurt to test that as well:

This electrical gremlin pops up on the forums every once in a while. The symptoms are always the same: the backlight goes out for a few seconds and then comes on again. So far I haven't read of anyone who fixed the issue. Either they are still pulling the fuses when parked, or they didn't bother to update the threads they started about the issue...

You may want to get in touch with Greg (TTTXGreg) who had the issue back in 2006. Maybe he recalls what he did to fix it.

The A1 general module (GM) is often referred to in case of this problem, but I believe it's completely unrelated. The consumer load cut-out has no relation with the A25 body electronics module (EKM) and instrument cluster. The odometer backlight is controlled by the instrument cluster which would be my main suspect, but it is of course possible external factors make the instrument cluster incorrectly turn on the backlight. The odometer backlight is linked directly to the MID (to adjust the MID's display brightness). Just to rule out the MID, remove it and test again.

Because you mention an issue with the ignition switch, rule out that one too. Simply unplug the entire switch (X33) or measure the voltages on the green, grey/white, black/yellow and violet wires from the ignition switch (to ground) with the ignition off. If any of those carries 12 V, or if the problem is resolved with the switch disconnected, the switch is broken.

If that's not it either, try to get hold of another instrument cluster. No need to code it to the car. It will show EEEE and the gauges will not work, but that's not important. Only the odometer backlight behavior is of interest. If the problem is now resolved, your instrument cluster is the culprit. If it's still there, it's probably the EKM...

soooo... that odometer light should stay off... aha... well - then I have that fault, too. damnit! My light is kinda indecisive. When the car is locked it sometimes goes off... for a while and then comes back on again. Maybe I need to measure my current drain.