On our 04 Imperial the zone 2 (potty room) pump is also the "stir" pump which circulates the hot water in the tank to keep it uniform in temp. It will run without the fan in zone 2 running. The problem you have is probably a stuck check valve as trainer explained. You should remove the cover and, with zone 2 heat selected and the fan blowing air, check to see if the pump is running.
On mine the zone 3 (bedroom) pump has failed and I am trying to find a replacement for less than the $400+ the mfgr wants for one.
Ron