What voltage are you using to pulse the solenoid? Do you know how much current it takes?
It's rated at 6VDC and 250ma.
is the foot switch a momentary type (in which case, can you tolerate a small current draw while the foot switch is held down), or is it push on/push off?
It's momentary type. As long as I keep it pressed, the circuit is closed. How small of a current draw do you suggest? A few micro amps is fine but if it's a few milli amps, that would greatly reduce battery life making this project not very practical.