@UPGrayd, from electrical measurements, taking things apart, etc., and with very similar symptoms to yours, I have almost certainly concluded that my fan motor is bad.
The key thing that is confusing your and my situations is that even with a failed motor (failed in that it will not spin when properly commanded to spin by the ECU), it will still bump a little sometimes upon startup.
My measurements and Foxwell active testing all seem to confirm that everything is working other than that the fan actually spins. I don't get any codes, warning messages, lights, etc. It just does not spin.
Also surprising is that even after failing to spin at the startup, it will continue to be commanded correctly during further operation. Why do the bump-and-spindown test, get a failure result, and then (1) don't report or silently log the failure, and (2) continue to command the fan to spin as if it had passed? But that's what it appears to do.
I can't find any info on the diesels, but I did confirm that ALL non-diesel E53s now use the same fan. 3.0i, all the way up to 4.8is.
From realoem:
https://www.realoem.com/bmw/enUS/sho...diagId=64_1087
BMW PN for the full assembly:
64546921381, which supersedes:
64546921940 (11/12/2001 — 08/16/2004)
64546919051 (06/01/2001 — 10/31/2001)
64506908124 (12/01/1999 — 06/20/2001)
64548380573 (10/01/1999 — 03/17/2000)
There was a recall back in the day, and the ...381 was installed when doing the recall service.
I think I fit the category of the aux fan being non-essential, but plan to replace it when convenient.