Final stage resistor
 

Two days ago my blower motor came on - on its own.. Ah I thought. The FSR has failed so I pulled the 30a fuse to stop the fan running.
Today the battery is flat. Is it possible for the FSR to drain the battery on its own?

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I am not sure if the FSR, with the related blower fan fuse removed, will drain the battery...But easy enough to check....charge the battery up and pull the FSR...

If not do a parasitic drain test...There are like 6-8 things that can drain a battery on an E53..

I had a similar experience with the battery draining on my mostly dormant 2001 3.0i.

Here are my notes on what I did to fix it until the next thing came along:

"HVAC Blower Final Stage Resistor - Twice while the car was in the driveway, the HVAC blower turned itself on with the key out. This is a classic symptom of the common failing FSR problem. Pulled fuse F64 from the glovebox fuse box (right most of the 4 big 50A fuses on the right side), which killed the blower. Bentley says the blower is the only thing on that circuit."

So the clearest mismatch between your situation and mine is that mine was a 50A fuse, not 30A. Maybe you pulled the wrong fuse?

It could have been a 50a didn't look properly but when it came out the blower stopped.
Something else odd I noticed was the little red LED next to the head unit right hand side control knob was flashing. As far as I remember it was always solid.

You didn't accidentally programme the vent timer (or aux vent.) to come on, did you? ;)



https://youtu.be/HVTHSY9-z4c

That crossed my mind but I hadn't touched the head unit. I was actually sat in the car when the blower came on. Key was in the ignition but turned off. That's when I noticed the flashing led.

Maybe try some of the things suggested.

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So I put a spare FSR last night and took the Ctek charger off. 50a fuse went back in.. Fan didn't come on and it started OK this morning. I will use it and then leave it for a few days on the drive to see what happens.
Tell you what tho - I'm glad I bought a jump starter pack last year. Topdon is the make but can't remember what power output. They are so handy. Highly recommend getting one.