my memory may be goofy on this... but isn't this a part of the starter relay setup? Seems like there is a separate circuit which feeds 12V on the coil side of the ballast resistor when in the "start" position (bypassing the resistor) and the circuit is fed by the relay.

I know I have encountered the opposite situation when the car starts and runs as long as you hold it on "start" but then stalls as soon as you release the key, which is what you get when the ballast resistor goes bad. Just extrapolating from that.