This is in the 240D (manual CC)

It sounds like a pigeon, and seems to be coming from behind the instrument cluster.
Like a whining gurgle? Kind of rhythmic, or maybe cyclic.

When I turn the compressor off it goes away.

Doesn't vary if I turn the compressor control knob up or down - if it is on, it makes the sound.

The speedo seems to dip slightly with each pigeon "coo".

A/C seems to be working, though maybe not quite as well. (It has been converted to 134a, so it isn't ever a freezer.

What should I look for?

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Current Mercedes
1979 maple yellow 240D 4-speed

Gone and fondly remembered:
1980 orient red 240D 4-speed

Gone and NOT fondly remembered:
1982 Chna Blue 300TD

Other car in the stable:
2013 VW Jetta Sportwagen TDI / 6-speed MT