My car thinks that the coolant is low

[Phil Strong]

After driving for almost 2 hours yesterday in my 89 80Q, the low coolant
light came on.  Pulled over, checked the coolant level and it might of been
just a tad low, so I added some more antifreeze/water and finished up the
last 20 miles of my trip.  The low coolant light still was on so drove
moderate the rest of the way.

I checked the coolant level again this morning and it seemed fine.  But
within 30 seconds of starting the car when the engine is either warm or
cold, the low coolant light comes on.  The car seemed to warm up as ussual,
but I decided that it would be a bad idea if I went for a driving test to
ckeck it out.

What's the deal here?  The coolant level is fine in the reservoir... so why
does the autocheck light come on saying that the coolant is low?  Is it
possible that the water pump died?  How do I check for this without risking
damaging my car?

Phil