The LED in my build stays on whether or not the input jack is plugged in. The switch turns it on and off, but the input jack does not switch the LED (and presumably the rest of the circuit) off. All wiring from switch to jacks is correct.
follow the leads to the LED and ask yourself why does this have power all the time? and how can I switch it on and off with the input jack? This is a simple lesson in troubleshooting and you'll be better at doing it after you get this one figured out. I'd check the input jack itself and see that it is switching the ground signal for your LED....
All wiring from switch to jacks is correct.
If it is intended that the LED is not getting current when the jack is unplugged?
You want a TRS jack, stereo.
You don't want ['switching jack' has the 'extra wiper' on the tip wiper, plug inserted = break contact.
Connect battery to Ring [middle]
Connect circuit to Sleeve.
A 1/4'' mono plug's sleeve will connect/disconnect the jacks R/S lugs, and make/break the battery circuit.