Are you sure it is on, or that something added is causing a backfeed on run/ shutdown? In other words, start with the engine off and do not crank. Turn the key to ACC and see if the ign system is getting power, AKA does the coil + have power? It should not.
It's either right in the switch or a wiring error that has somehow interconnected the ign "run" and ACC busses.
So first thing to do is disconnect the key, turn it to ACC and do some ohmeter / continuity checks
From BATT into key:
"run" (usually dark blu) (IGN1)should ONLY be hot in the run position. It should go dead with key twisted to start, and dead in ACC position
bypass (usually brown, the ballast bypass) IGN2 should only be hot from BAT when key is twisted to start. THIS IS a different set of contacts from the "start" circuit to prevent backfeed
START, (usuually yellow) from BAT should only be "hot" with key twisted to start
ACC should be hot with key either in "run" or ACC and in no other position.
With this checked out, you have work ahead, as no idea at what point this could have been cross connected.
One thing you could do is separate the bulkhead connector. Get a diagram and identify what comes through there and see if pulling that fixed the problem. Bear in mind that when you separate the bulkhead connector, the ammeter circuit will be affected