If you are talking about the Starter Relay it only has terminals with constant power or power when cranking only. It is not powered when in the run position of the ignition switch.

The ignition should be powered when cranking and when in the run position.

I would suggest using the the existing ballast resistor power but probably before the resistor and not after it depending on the voltage required.

The ballast resistor is powered at cranking and running.