Have you checked what happens at the switch terminals with a multimeter, when you action the switch back and forth - ie is the centre terminal the common - and does continuity between centre and outside terminals occur as you switch the switch....

 

Yes, that is how that switch is set up (center is common). Since this is the case, how do you make this switch work with two power sources to one load?

 

Please excuse my obvious question, but your switch has exactly three terminals? I ask because I thought I saw four in your picture.

And none of the connections are touching? It looks like the wires from the center and rightmost terminals may be shorted together.

 

Yes, the switch has exactly three terminal, and none of the connections are touching.

 

Yes!! Got it working. Turns out it was a bad connection. Thanks for all the help everybody!

 

Turns out it was a bad connection.

Told you so!

Good job getting it working. Score one for persistence.