If that orange wire indeed does go from the light switch (which is missing) to the brake switch, then why do my brake lights work with the headlights off?

Can I simply pull that orange wire off the brake switch, and add a new one from the brake switch to the light switch?

I'll go pick up an ohmeter and track that wire down later today. Been getting "the hairy eyeball" from the wife cause I'm working on the truck too much lately!