How can I actuate a relay coil from a headphone jack's internal SPDT?
You want jack "C" at the bottom of this link: http://en.wikipedia.org/wiki/Phone_connector_%28audio%29

The tip and sleeve switches are electrically isolated from the plug so signal is transmitted uninterrupted.

There are 1/4" jacks here (http://www.minute-man.com/acatalog/1_4__Stereo_Jacks.html) that do this. I'm sure they have 1/8" jacks that do the same thing, but I didn't look.

I was looking for the same thing, but for switching inputs based on whether the plug was inserted in the effects return on a tube guitar amp. Can't be puttin' that signal level into the common when someone has it in their hands!