Finally found what I was looking for in the 1986 W124 "Introduction into service" manual (this has all the information on the W124 as a new model). On page 283, it says that "the auxiliary coolant pump (M13) . . . runs in the heating mode, when the monovalve is either completely open or cycling."
I infer from this that on a hot day, when you are using the a/c, the aux pump will not be running. The aux pump gets +12 Volts from Fuse 7 and is grounded through the Push-Button Unit, which turns it on and off as needed.
"Buster" in the '95
Our all-biodiesel family
1995 E300D (W124) 201,000 miles My car
1996 E300D (W210) 289,000 miles Wife's car
"Politicians are the same all over the world;
we build bridges where there aren't any rivers."
-- Nikita S. Khrushchev