12.6 is a full charge on a good battery. A bit higher is ok. If the battery is holding that, and it should hold it for days at least with nothing connected, then you're ok there.
Pulling down like that overnight isn't normal.
Most likely... You have a light on, HL motor problem, or a bad alternator.
There are more notes on this in my cave. You'll need a meter with a 10 amp circuit.
It is sometimes possible to recover a battery that has been pulled really low but you have to be careful. It's really easy to boil a cell if it's done wrong. If you try to run a car with such a battery in it you can kill the alternator. (A battery below 11 volts should always be charged before trying to run the car.)
Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
The Ogre's Fiero Cave (It's also at the top of every forum page...)