SPDT simulation, relay, optocoupler or something else?
You can use a sealed signal relay (&lt; 2A) such as an Omron G6. There are other options, but the relay is straightforward and should just work. 
A 1/4" stereo plug has three electrically isolated parts- the tip, the ring and the sleeve (image from this site, ignore the balanced, hot/cold designations).  




It's not entirely clear from the verbal description how the switch is to be connected other than that the N.O. contact goes to the tip. I could make an educated guess (N.C. to ring and common to sleeve), but it would be much better to get even a hand scrawled schematic from the supplier.