I think I figured it out. The hot water/aux heating unit has it's own
flat coil in the top of the air handler above the blower and just below
where the central air duct connects. Both of the hoses from the water
heater attach to this coil.

The lower A-coil is for the heatpump only and is only working on one
side of the A. The side that works gets cold very quickly when the
unit comes on. The other side is clogged or damaged and has no coolant
circulating. That side does not change temp at all when the unit is
running.

Time to talk to my maintenance guy.

Thanks for the help.

Neal B.
Richmond, VA