72 Demon fuse block wire

DETAILS!! Year, make, model

What do you mean, "exterior lighting?" Parking lights, etc? Most? All? of the exterior lighting comes through the light switch, the brake switch, and the turn signal circuit.

That wire is either added or hacked. Where does the end in the fuse panel come from? If it is connected to the load side of a fuse, look that fuse up in your manual and see what all it lists for that fuse's load