My 67 Barracuda has the same system. One single wire goes to the ignition switch or could also go to the wiper switch and the one that have the splice, goes the rear lights harness and to the starter relay (only if it has the clutch safety neutral switch). The one that go to the ignition/wiper switch will give "juice" to it, so when you go to reverse gear, the internals will "connect" both ends and will complete the circuit and will turn the backup lights "on" and the internal light also. You will not use the one going to the relay, unless you have the "safety neutral switch" in your clutch pedal.