2014 BMW 328xi Sport Wagon, 1984 Avanti 5.0 HO V8
While it may not explain the whole story, the battery voltage you measured sounds rather low, if it was indeed a no-load measurement. A healthy battery with a full charge should read around 14.4 volts or so.
Not true... 12.5v to 12.7v is normal for a fully charged battery measured with the engine not running. 14.4v is typical with the engine running, but the higher voltage comes from the alternator, not the battery.