I think 196773 is right. Sounds like the limit switch on the headlight assembly it misbehaving and/or the terminals are corroded. The limit switches are easy to test. All four switches are identical. Each switch has three terminals: One terminal (farthest back on switch case) goes to a ground and should always face downward when installed, while the two other terminals which are closer to the button side of the switch case are connected to the wire harness ( I call them wire harness terminals) When the button is NOT pressed the wire harness terminals are connected to each other, as a result a multi-meter should read zero Ohms across the harness terminals when NOT depressed. When the button is depressed the ground terminal and the terminal on the opposite side of the switch case are connected, while the wire harness terminal next to the ground is disconnected. As a result the a multi-meter should read zero Ohms across the ground and opposite side harness terminal when the button is pressed.
67 RS Convertible, 355ci, 650cfm, 5-speed, 12-bolt, 3.90 gears. 12.7 @ 110 mph