I am assuming from your previous posts your starter switch is a push button with two terminals and you can run the starter with the ignition off. The first terminal connects to the battery and is hot all the time. The second terminal goes to the starter solenoid. It sounds like you have your ballast resistor bypass wired to the switch too. It should be wired to the same terminal as the wire that goes to the solenoid.
The alternator "idiot" light is in addition to and not related to the ballast resistor. I think you said you bought your harness? They may have already dealt with the "no shut off" problem.
Experiment by disconnecting that second wire to the coil first.
