bluejets:
Op's line voltage is 120vac.
12v not much use.
That depends on the application, now doesn't it.
It is much more useful than a 220v relay with 120v
If, for instance, the OP wanted to have a relay that was powered all the time.
all that is needed is a simple wall-wart to the relay.
and, if for example, then there is a loss of power, the relay fails to the un-energized state and the battery is now connected by the contacts to the LED lights.
When power is restored, the wall wart will recive power, then energize the coil and the relay contacts will open and the LED battery will be disconnected.
by connecting the battery charger to the same relay, the battery would be charging when there is mains power, and then light the LED when there is a power loss.
in the above example, the 12V power could be the source for the battery charger as well.