I have no coolant flow through my heater core, but engine does not overheat.

What is your question?

This is on my 92 Safari, not a 91 Safari! I have flushed my coolant system as well as flushed the heater core. I disconnected the hose from the "Y" connector on top of the water pump and found that there is no water flowing out of the water pump.

How long has your 1992 GMC Safari had this problem?

Several weeks