12 volts of AC? Far too much. I don't think that's even possible. 12 volts of DC is too little. DC voltage should be more like 14.Do I need to take the cable off the alternator to check? I checked with cable on the alternator and had 12 volts
RUN THE ENGINE WITH ALL CABLES CONNECTED. Set voltmeter to AC volts, and connect to the alternator output stud, and alternator ground. Measure AC voltage (often called "ripple" when talking about automotive alternators.)
Shut off engine. Charge battery with alternator + cable disconnected. When battery is FULLY CHARGED (Measures 12.6--12.7 volts DC after surface charge has been removed. (Will measure ~13 volts or more with the surface charge) see how long the battery remains at ~12.6 volts DC with the alternator + cable removed.
If the battery stays fully charged for a long time with the cable removed, but discharges rapidly with the cable connected, you've got bad diodes in the alternator.
But, again, four guys say that the diodes are fine.
You could have a parasitic drain in some other circuit, though. I've seen batteries discharge through the conductive slime that accumulates on the plastic of the battery case.