Generally a typical fuzz face circuit it draws so little current that a battery inside it will last after you change all your teeth on a dentist. most guitar pedals using a stereo input so when you disconnect your guitar cable it brakes the psu circuit for longer battery life. That can be achieved by soldering the "-"of the battery and power jack to the ring of your input jack on the pedal, removing the cable will stop the powering to the circuit..simple yet effective.
https://lh5.googleusercontent.com/-NcBSbulkwTo/UJHt2m1ZCKI/AAAAAAAAKMs/E-9fsZF7HI4/s398/trs-explanation.jpg
https://lh5.googleusercontent.com/-NcBSbulkwTo/UJHt2m1ZCKI/AAAAAAAAKMs/E-9fsZF7HI4/s398/trs-explanation.jpg