easiest way to tell if water pump is working is to run engine until at running temp. then carefully remove radiator cap. with someone slightly reving engine, look into radiator. if the pump and thermostat are working correctly, you will see the coolant moving(circulating) in the radiator
No circulation.
how do you tell if your fuel pump is working
Use a digital multimeter and test it for resistance.
if your water pump fails, engine will overheat. You will have no heat in vehicle.
If you have oil pressure it is working.
Water pump shaft loose? Water pump leaking? Water circulating in coolant system?
get out of your car find it turn on your car and get out feel the pump if it vibrates it is working if not get a new one
It is rare for a water pump not to work however a water pump going bad will leak coolant and can be noisy from bad bearings.
My guess is low or no oil pressure.
Wait until the thermostat opens , so the top radiator hose is hot , then squeeze the radiator hose and then stop squeezing - if the water pump is working you will feel a surge of coolant through the hose if the impeller inside the water pump is fine ( I'm assuming that there is no squealing sound or coolant leaking from the weep hole of the water pump )
I'm not a mechanic / technician but the way that I tell the water pump is working is : I wait until the engine thermostat is open ( the top radiator hose is hot ) and without catching anything in a moving belt I gently squeeze the top radiator hose and then release it slightly , you should feel a engine coolant surge
A fuel pressure test can determine if the pump is working properly or not.