I don't know about the GT but in the headlight housing on my G5, there is one gray wire.
It's purpose is to be attached to the running light bulb that is in the lower part of the headlight reflector on those old lights that use a small removable headlight bulb (not a sealed beam type).
Because the 7 inch headlight I installed doesn't have that little running light in its reflector, the gray wire went unused until I added a after market voltage indicator.
I used the gray wire to power the indicator.
Because the running light is on when the 'parking lights' or the actual headlight is on, a glance at my voltage indicator tells me if I have turned on at least my parking lights.
If I don't turn on the parking lights or headlight when the engine is running, the voltage meter is not lit.
Link to the voltage indicator I installed.
https://forum.classicmotorworks.com/index.php/topic,12424.msg137999.html#msg137999