Your '67 must have an option not generally seen on cars until several decades later. Modern cars, some at least, with a starter button and you just leave the "key"in your pocket require the brake to be held on for it to start.
I take it the car is an auto? Fox bodied manual Mustangs had a switch on the clutch pedal that prevented starting unless the clutch pedal was depressed. Autos just had a normal nss.
Unless someone has wired in some modern trickery to the starting circuit, I wonder if the brake pedal is interfering with some part of the wiring such that the starting circuit is only complete with the pedal depressed, something got pinched or something? Anyway, that's a weird one, even on these old cars that often throw up electrical issues.
Hope you get it sorted.