Ok… so bear with me… I should test it by taking a single piece of wire and connect the two terminals you mention… but then what? Ie, how will I know it's worked (or not)?
If it does work, and we snip off the jack, will there be more than one wire inside? Will it matter which goes to GND and which goes to S?
EDIT: is there any chance the problem is with the switch part of the switch? Or the way we are using it? (Does it have to be held down for a certain amount of time for the Iowa Linc to pick it up, for example? Although again : the LED flashes even with the quickest tap.) Or any way to troubleshoot that before I potentially cut off its jack? (Although I suppose if it still doesn't work with the I/O Linc we can always rewire the jack back on…)