Starter keeps starting!...

Get a remote starter switch, with key in run, hook it up properly and push the button.

My bet is you are back feeding the ignition system run power, back to the starter realy.
Okay now that is exactly my next thought here... So I'm testing all these wires with a nice power supply unit and I test the coil wire and it's getting juice to the coil when I hit the the start but it's not getting juice on the run position? So I went ahead and spliced (I had to look at my schematics).. I also ran the cruise control wire which I wasn't using for a constant on power to the coil as well. I think you may have something right there where it's just backlighting the ignition?
I just wasn't sure how the coil would get power if there was nothing while it was on the on position?...