So, basically the input is switched to one of two outputs and the LED is illuminated under the selected output? And probably the switch is an ON-OFF switch and not momentary.
Confusion is: Why is the input a stereo jack used?
Assume for the moment, that the input jack is supposed to be mono, but a stereo jack was used instead (hopefully I'm right).
A phone plug consists of SLEAVE, TIP and RING; A mono plug would have SLEAVE and TIP
Also look here:
Tip and ring - Wikipedia, the free encyclopedia for a definition of TIP, RING and SLEAVE.
1) Make sure all of the SLEAVES are connected together of all three jacks (your black wire).
2) Insert a MONO plug into the stereo jack. TIP will be connected to a contact. Make sure there is a wire connected to this contact.
That picture is a "wiring diagram" and not a schematic. I personally find wiring diagrams more difficult, because you can't figure out the functionality.
I'm just having visualizing the metal contacts and the terminals because I'm deprived from all views.
Hopefully, I'm correct in the description of the operation and you can trace it out.