As the topic title says I have installed the Mechanical GT headlight pop up system.
What have people done to hook up the headlights since you have a bunch of wiring for the motors that no longer needed? Is it possible to run the headlamps and fog lights from the same switch? TIA for your input

I'd use shrink tube to cover the wires and keep anything from grounding.
As far as running the headlights and fog lights on the same switch I'd say no. You could run a relay to the fog lights off the same switch just not the lights.

I did as above - preserved the no longer needed stock wiring as best I could, insulated any exposed ends/connectors and tucked it away. As I recall you can also ditch a couple fuses as well as the relays for the old motors. (In full track config actually I used to run my car off 1-2 fuses total.)

My car has the factory fog lamps and separate switch and I would not try to combine or simplify those circuits further. I suppose if desired you could probably wire one switch to control two (or more) relays for both sets of lights. As long as you can power them adequately and the hot wires can handle the load.

Pull'em from the harness... it's a short run.