If it cranks, the neutral safety switch is functioning. And it's not the resistor itself, or it wouldn't run at all. The ballast resistor run circuit (blue wire) is only hot in the run posistion. It is not hot during crank. The ballast resistor feed in the crank position comes from the brown wire. By jumping the solenoid it is not using the crank circuit (brown wire) to feed the coil. Check for voltage at the coil + during crank. If it has none or is low investigate the crank cicuit from the ignition switch, thru the ballast output terminal, then to the coil. A second possibility is that it is fuel related. After 2 pumps and getting out to open the hood, then jumping the solenoid may give the fuel time to vaporize. If the wiring is good. Wait 30-45 seconds after you pump it before cranking.
Doug
Good advice from DVW and Cab. My only comment would be two pumps sound a bit excessive for a warm motor. Maybe depress the pedal 1/4 to 1/2 at most and hit the key.
If no help then definitely head straight to the voltage checks
keep us posted