The most common failure mechanism is for the climate control servo to
go bad.  This controls the heater core water flow, vacuum flaps for the
heat/ac system, compressor, fans speeds, etc.   One failure mechanism
is for the lower plastic case to crack and leak water into the
motor/grear train and destroy it.  If you see coolant dripping from it,
it's shot.  It also has a feedback potentiometer in it that's part of
the resistor chain that maintainst the set temp.  Like all pots, it is
subject to dirt/bad spot's developing, particularly if it hasn't been
worked in awhile.  That's why it's advisable to cycle the system from
max heat to max cool about once a month.

Another common failure is the amp module that drives the servo.  The
servo is located in the engine compartment, pass side, near the
firewall.  The amp is directly behind the glove compartment.  These are
easily replaced and go for about $100

If you get to the point where you want to try to directly drive the
servo, you can do that with a 9V household battery.  You need to locate
the two connectors on the servo that run the motor inside the servo.
They can be found on the service diagram.  Disconnect the two wiring
harnesses from the servo  Applying the battery in one direction will
wind the motor all the way to full cool, reverse the polarity for full
heat.  And only apply it for a short period, if it's working, you will
hear the motor whir.  When it stops, its at the end of its travel,
(full heat or cool) so dont leave the battery connected or it will burn
out the motor.   If it's an issue with the pot, cycling it back and
forth a few times may restore it.

You can also measure the resistance of the pot through the terminals to
verify it that's the problem.  If it is, it's possible to remove the
top of the servo and spray cleaner into the pot.  Beyond that, the rest
of the servo is beyond the servicing of mere mortals.

If you need a new one, George Murphy at Performance Analysis, in TN
sells rebuilt ones.  He replaces the lower plastic housing with an
aluminum one.  I think he charges $5-600 for one.  However, beyond the
one yr warranty, he offers lifetime repair for $100, which I think
makes it a good deal.   I've had one for about 2 yrs now and it's been
working fine.  Also, T.G. said he was putting one of the new digital
ones, that replaces the whole craptacular system of servo and amp, so
you might want to check with him if it turns out you need one.  I think
those were a few hundred $$$ more.

Good luck!

Thanks to all for your advice.  The unit has fortunately broken loose and
is working OK now (the AC still needs to be recharged / converted).

The vacuum pump that failed was a piston type.  It might have been the
original with 250M miles.  The spring and lever are missing (probably in
the sump or out the exhaust pipe) and the pivot bracket was broken.  I
had just had the timing chain changed a month before, but the parts got
tangled in the chain and it jumped time.  My son, who was driving it,
said it had chugged for about 20 seconds as he tried to turn around and
head for home.  Then there was a frighteningly loud crack followed by
silence as he coasted to a stop.  The autopsy found that the timing chain
was broken, the camshaft was in three equal length pieces, and the front
three aluminum cam bearing towers were broken. No 2 cylinder top shows
just a light scratch corresponding to the valve that it met.  I think
that the cam towers are probably engineered to fail first to save the
bottom end.  I will further tear the block down to be ready for a
complete overhaul if the replacement 'used' engine shows signs of
eventual weakness.