On anydriving mode i used to listen to the sound with AC or not. Mostly uphill and low revs. As my vitz is 1999 so i dont really have a Rpm guage as it comes with a digital speed o meter.Second yes, it is a rotary part with kind of fan type that goes into the water assembly. Water assembly needs cleaning too doesn't need to be changed (If not broken or leaked). Other than that the gasket came with the waterpump was thin so i thought about it and got me self a thicker gasket, the secondary gasket at the water inlet was checked as well and since then well everything is pretty good. Ran 40k Km after that. No noise what so ever.
May be water body and water pump are the same OR lets say, water body is actually the water assembly. But water assembly.
What i know is this is the water pump that i replaced.
and there you can see the water assembly/Water pump cover which i dont think you are referring to.