Edit: I think I misread your question, your only water pressure is from gravity? I assumed your water supply was pressurized. You want something to sense the water level in the tank to cycle the pump, not pressure or flow related.
Sensing water flow is more complicated than just sensing water pressure. A SPDT water pressure switch can be installed at the water pump inlet to power the pump when it senses water pressure at the pump, and cuts power if it doesn't sense water pressure. This way the pump always runs when the water supply is on, and never runs when the water supply is off.
Ideally you'd have an electric circuit that opens a solenoid water valve for your supply and powers the pump at the same time, being activated by a water level float or sensor in your tank.
I use the same switch for my reverse osmosis water filter. I have an AquaTec SPDT pressure switch that prevents the booster pump from running if there is less than 20 psi supply water pressure. That way it never runs if there is a problem with the supply, because it would run nonstop and eventually burn out the booster. Technically it wouldn't run dry, because air would have to be introduced into the system first which would be unlikely.