The way I would think it would work(and I could be wrong) is the fuel stop gets its power through the fuel stop relay. Because the engine continues to run, the fuel stop must be getting power from another circuit. (maybe a short from the AC blower) You could start pulling fuses with the engine running. If it stops that is the circuit that is feeding the fuel stop.
"he told me if I disconnected the fuel stop solenoid and the engine kept running then the solenoid was bad because it was staying stuck open."
This isn't the case. Correct? When you unplug the sol. the engine stops, yes?
With the ign off, there should be no voltage at the solenoid. I would guess is that you find the opposite.