Looking for suggestions where to start troubleshooting. Scenario: I start the car, drive the car no problem. Turn off and return the key..... Car remains running! Turn off the headlights and the car turns off. Lights are back feeding the ignition somehow.

 

You don't give the model year for your Z, so I'll use my 2005 as a reference, but here are a couple of things to consider. Power for the ignition coils comes from the IPDM E/R through the ECM relay. The IPDM E/R is the fuse block mounted just outboard of the battery. The IPDM E/R also contains the headlight high and low beam relays. It sounds like your ECM relay may be staying energized when the key is turned off. However, power to the injectors comes directly from the ignition switch through a 10 Amp fuse, so you should start looking at that switch first.

 

is the cars name Christine by chance?