No float/safety device in fresh water tanks to prevent pump from running
Rv Pumps are diaphragm pumps and can be run dry w/o harm
But if your are connected to 'city water' and water supply pressure is higher than pump pressure switch then pump will not try to run----no reason for it too
as they are 'on demand' pumps
But if you are not connected//no water pressure then pump should run.......wouldn't pump anything cause fresh water tank is empty (that is where pump sucks water from)
In that case:
Pump pressure switch stuck OPEN
Pump 12V DC Fuse blown
Pump controller failed (if you have several momentary on/off switches)
Question.........
WHY are you trying to run pump with fresh water tank empty in first place :H