Ignition Switch Changeout

I thought the same thing but with a ballast resistor, it will start and then quit when you let the switch go to run position. Reason being is the ballast is bypassed in crank but current flows through it when you go to run so a bad ballast will kill a started engine. Perhaps the OP was not written correctly? Cause yeah, if it starts and then quits when you let up, thats for sure a ballast.
Duh... You got me!