I think my dashboard is haunted

When I shut off the ignition in my 88 735iL, I hear a whirring sound with a quiet buzz for about ~10 seconds. The buzz continues and then there are 6 more ~1 second whirs, the buzz stops , one more short whir and we're done.
As near as I can place it it is coming from the center of the dash. I would assume something to do with the climate control which is all off right now.
Can anyone exorcise this demon?
Thanks in advance

I have yet to figure this out too...but as far as I figure, it's normal operation, so I wouldn't be to concerned about it.

Thanks. I thought I was losing what was left of my mind.