One way:
Have the wall adapter go thru a diode to the Barrel Jack connector, and have your lower voltage battery go thru a diode to the barrel jack connecter.
When the wall adapter voltage goes away the battery will kick in.
One way:
Have the wall adapter go thru a diode to the Barrel Jack connector, and have your lower voltage battery go thru a diode to the barrel jack connecter.
When the wall adapter voltage goes away the battery will kick in.