Andy,
Having your battery voltage, settle to 12.5 volts after the engine turns off is pretty normal. If it sets for a few hours, it's not uncommon for the battery voltage to drop to 12.2 or so. Usually with the engine running at reasonable revs, you should see 13.5 to 14 volts at the battery indicating that the alternator is charging. As David notes the duceleir alternator is known to not have enough power and to be flaky. Hopefully, changing the alternator will solve the issue.
Ron