This circuit simply switches power from terminal 87 to terminal 30 when 12 V is applied to terminal 85.
Yes, a clean 12V needs to be pulled from a battery to terminal 87.
You wire terminal 30 to the PP purple wire. The old purple wire can simply be "nutted" off - it was the 12V power supply from the PP harness.
You wire terminal 86 to ground. It doesn't have to be ground on the tach. If you chose to wire to ground on the tach, don't remove the wire that is already there (you'd be removing the ground, which is what you are trying to steal). He is basically just using the ground on the tach as a convenient place to steal a ground. I ran mine to a clean ground run from the battery.
The remaining wire is a new clean run to the ignition switch, and applies 12V to the "switch" in the relay whenever the key is in the ACC, RUN, or START positions.
For the logic module, you're doing more of the same. You are breaking the 12V feed to the logic module, and providing a new power source from terminal 30. So you'd clip the purple wire, cap off the end that doesn't go to the logic module, and run an additional lead from terminal 30 to the purple wire that feeds into the logic module.