Does the SAP make any noise?
 

I can hear the secondary air pump cut on for maybe 10-20 seconds on cold starts, and it's noticeable, but not loud. I was wondering if it is normal for it to be audible at all, or if mine might be going bad. I haven't had the vehicle long enough to notice a change, but have since been more attuned to the things to look out for and noticed that whining sound as at least being fairly distinct among the symphony of sounds back there in the morning.

Ill have a look at it when the car gets back from the paintshop at weekend , but if its anything like other German cars of the same era it will be an assembly of two as tic halves riveted together .
The rivets corrode and the seal is lost ...
It is an easy job to remove it and drill out the rivets , clean it , then reseal using nuts and bolts .
Iirc you will drill 6mm and use 5mm bolts to "re-clamp".

Lots of guys in non-smog states remove it all together ...

Yes, the SAI pump makes noise for 60 to 90 seconds at cold start up.

mine too and it stops at the end of my driveway