Ask the folks at mbcoupes.com

Sounds to me an awful lot like a blower motos. If yours is original
then at this age you can be expecting to replace it soon.

There are two common fialure modes with this part (which is the same
on all W126 chassis, coupes or sedans) and they are 1) there's a felt
pad at the bottom of the blower motor shaft. If it's completely dry
then a small squirt of tranny fluid may help a lot and 2) the carbon
brushes, when they are totally worn out will be gone and the metal
holders will dig into the motor shaft and make this noise. There's
no easy way to replace these brushes, you have to get a new blower
motor. Used ones will be no better, you need a new one, they're about
$120 or something like that.

The first thing you'll want to do is find out where the noise comes
from though, get a philips screwdriver and undo the 4 screws that
hold the upholstered kick panel in place and when it's making that
noise see if you can find which bit is doing it. There is another
black plastic panel between you and the guts up there, just take it
out and you'll now have access to the blower motor (which is 99% of the
time the problem) and related electronic modules (which I've never heard
failing).

I had the same problem with my '91 300D 2.5.  It happened in
cold weather conditions, and was triggered by applying the
brakes.  The colder the ambient temperature, the greater the
likelihood that the squealing would be continuous (and painful
to listen to).

The difference was that in my car's case, turning off the climate
control made the noise stop.  

Geoff