Your picture doesn’t clearly indicate where that connector comes from or the colors of the wires. In 68 there is a 3 female accessory plug that connects to the Fuse box. It is normally yellow though. It is used to power a number of optional accessories and is power when the Key is in Run or Accessory position.

The Rear defogger, A/C, Safety Convenience warning Lamps, speed control, tilt column all get power from the Accesories connector.

Follow the wires and show where it connects. Clean it off and get us the correct colors.

Best I can guess the wires are Light Blue with Red stripe. This is the color code for instrument lighting. This makes sense as there is a 3 female pin connector in that circuit.

To Confirm it, with lights on, see if you get 12V on it. Then check for no voltage with lights off. Then with the fuze removed check for continuity with the bottom connector for the 2.5 Amp Fuze.

 

What are the colors of the wires going into the connector. Insulation color plus stripe color (if any)

 

Hard to tell what the wire colors are, but here's a pretty detailed colorized wiring diagram...

'68 Wiring Diagram