9v Switch Help

[Salix12]

I have a 9v train layout similar to this.  I have two trains, one train parked in the green box and one train in the purple box.  I am trying to run one train at a time by using the switch tracks to only allow the electrical current to go through the aligned track.  Any ideas on how to do this?  I have tried to take apart a switch, but couldn't quite figure it out.

[Stereo]

My understanding of the switches is that the outer 2 rails are always energized, but the 2 that cross in the switch get switched, so you just need to switch both switches at the same time, and have the power supply somewhere else in the loop.  I know that'll work for stopping a train on your purple track, less sure if it's symmetric to green as well.