Probably not the wisest of methods but the set up of the footswitch was just one I spotted on Google images and I just ran with it!
But to answer the question as to where that wire's going - it's going from the positive lug on the DC Jack, to that top right pole, then the middle right lug (LED) goes into a 2.2k Resistor, into the LED anode (just soldered on component to component) then it is attached to another wire, which runs to ground.
I'll grab a photo of it asap, apologies. But I threw the explanation in to hopefully illuminate where that's going.