How to determine if water pump is working
2 Answers
Check for coolant circulation. You might be a to take heater hose return line to the engine loose, Take it loose at engine not heater core, bump the starter, any coolant flow? If you have radiator cap on radiator, remove it on cool engine, If you can see coolant, drain coolant down till you can see coolant passage, start the engine, you'll probably have to wait a bit for the thermostat to open, than watch for coolant flow from coolant passage in radiator. Just some possibilities to check flow.
If you have coolant in there, and not rusty water; and if it isn't making a terrible noise, then you can be assured that it is working. If you have, or did at one time have, rusty plain water as the coolant, THEN it is possible for your water pump head to spin off the shaft. I have see it twice. That is the only way the water pump "stops working".