Switch battery usage off when jack 3.5mm is not inserted
You can buy 3.5mm jacks that include built-in switch(es).  They will have separate connections for this switch, so you can wire your battery up through it.
There are three common types.  One where a switch is opened when the plug is inserted, on where the switch closes when the plug is inserted, and ones that have both.
The easiest would be to use the type where a contact is made when the plug is inserted.  Just wire up on of the leads to your battery through this switch.
Get one with an isolated normally-open switch.  Something like this:

Disconnect one side of your battery, and hook up the two ends to pins 5 and 6 and you are good to go.