From ign switch yes, is as you mentioned, but once both circuits are conected to the ballast, both circuits are hot, just at diff voltage rates ( selected from the ign switch ). The Ballast is a "virtual" splice.

When in ign1 12 volts is being sourced from ign switch, ign 2 gets 4-9 volts from same circuit throught the ballast in RUN position

When in ign 2 12 volst is being sourced from ign switch, ign 1 gets 4-9 volts from same circuit, throught the ballast in START position.

And that's how the ECU even is sourced from ign 1, it gets still power while cranking ( same as the cluster brake bulb )

And for the same reason, the coil gets the power in both positions ( so allways hot ) no matter the ign switch position, but just at diff voltage rates.

Think on it