I'd suspect the fuel solenoid as well... . first thing to do is make sure the two wires that connect to it are in good condition/tight... .
If they are ok, then, as suggested, you could remove the solenoid and pull out the rubber tipped plunger and spring, then re-install the solenoid.
As mentioned you'll need to use the manual shutdown lever on the pump for the time being, until you see if this fixes the problem and, until you get a new solenoid.
pb... .