Switch between 2 power supply feeds without device losing power
It sounds like someone installed a "double throw" switch. (aka three way switch)

 

Consider the circuit on the right. The red light is the one connected to your exterior light. And the other wire connected to the green light (in the image) is the extra circuit that goes nowhere. 

What I would do is disconnect the wire on the switch that goes to the green light (the one that goes nowhere) and connect it to the power feeding the switch. (the left side of the switch) You then would have continuous power on that line regardless of the switch position. This would be a lot simpler than trying to cobble something together as you described above. While it is an option I would prefer the simpler approach.