If your seat switch is working fine, then it's probably the operator safety module. That's a fancy word for an encapsulated module that does about the same thing as a relay. However NH wants about $245 for that module. They are holding you up without a gun. It's not the dealer's doin' it to you, but New Holland and probably Shibaura too. Your switch solution is a good backup, but make sure you pulled 12 volts from a line with a fuse in it. If that fuel solenoid ever shorts out, you'd have a fire on your hands in an unfused circuit. If nothing else, buy an inline fuse from any parts store and put it in the wire. 5 amps should be plenty.