BTW,

flybye, you need to rule out the FSR first.
When the FSR fails, it usually fails in the "ON" mode, in which case the blower motor runs all the time, draining the battery.
However, it can be "OFF" too, in that case blower motor does not run.

So, get a used FSR (BMW used) from ebay for $15, swap it and see what happens.

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1998 E39 528i 5sp MT
2006 E53 X5 3.0 6sp MT