looks like a 12v switch with a maximum 15mA current... A simple 12v 5 pole relay will switch the 110v .. All you need is a AC/DC convertor ( wallwart ) or we call a "12vdc mains adapter" and use the switch to drive the relay..
Where is the pump suction connected to ?
Is it to the street mains ? (illegal) or is it from a reservoir filled by the street mains ?
If a reservoir; a paddle pushed by the water inflow at the filling pipe can turn off the pump when there is no flow.
That is not right. "if there is no water" where? In the reservoir ?
"There is no water" is not "there is no flow"
Where is the flow you want to detect ? At the pump outlet or the reservoir inlet ?
Water can be flowing into a nearly empty reservoir with too low level to be pumped.
The correct way is to use a float switch in the reservoir that will disable the pump when level is too low.
I pull water out of the ground and store it in a tank for use later. This switch measures the pressure at the tank and turns the pump on if the pressure is below 30 and turns off the pump if the pressure is above 50 pounds.
If the ground water is gone the pump runs dry and burns up. "Water Pressure Switch - 30/50 psi with Low Pressure Cut Off" This switch is like the first one (on at 30, off at 50) but it has a "low pressure cut off" function. If there is no water, the pressure drops below 10 and the power is turned off. There is a lever on the right side. To start you must push by hand and hold until the pressure gets above 10, then release and leave. If the water is all gone the pressure is below 10 and the switch will stop and wait for you to start the pump again.
This is what I am using. I also use a "float switch" like in post #4.