Looking for a current-actuated timer switch
What you want is a current transducer with a relay output.
I use these to stop motors driving conveyor belts if the drive chain or belt breaks the load drops the current transformer senses the drop and trips a relay. Stopping the motor
The ones I use are fairly expensive AcuAMP act200-10-s
0-10v output  0-100 amp range  96$
I know automation direct carries them I use these on small motors in about 20 places in the mill.
No interest in automation direct I use there products.
The sensor is adjusted for the load and when the pump runs dry the current drops and sets the output a relay is what I use to interrupt the motor.
This could be used but a low level high level setup would be cheaper and make more sense.
Edit added for another method of control.
you could just turn off for a delay then pulse the pump if current high it keeps running if still dry it would shutdown.