I just went outside tried running a wire between the two ballast connectors and tapped into that with the computer and ignition. The car started right up and ran fine. However, I had run the white wire off of the alternator into that same wire at an earlier point, so I couldn't kill the car, lol. I cut the alternator wire off and started thinking about it more. Based on Lefty's post, I went ahead and just hooked up the ballast resistor. Then I ran the computer and ignition into the old wire that went into the external regulator because it was now a "switched" ignition. Started up and shut down great.

This is the confusing part for me though. I didn't have the alternator harness white wire hooked into anything and the car was charging. The white wire ran into a small light light, and it was lit up. Should I just leave the white wire going into the small light and nothing else? Based on the diagrams I have seen, the white wire from the alternator harness should run into a light to make the alternator charge and then run into a switched ignition source.