if you are reading 12.4 on a battery it is not fully charged, or it's damaged.
a fully charged battery should read 12.7 or higher. odds are good that your alternator is not fully charging the battery, or the battery is in need of replacement. have it thoroughly checked by a chain store.
before having it checked, I'd disconnect the neg terminal, and connect a trickle charger 2amps or so for 24 hours. then check the battery voltage. it should read 13.2-13.8 then connect the Neg terminal and turn on the headlights for 5 minutes. then disconnect the neg terminal again and test the voltage. if it's not reading 12.7 the battery is suspect.

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John HAUL AWAY, OR CRUSHED CARS!!! HELP ME keep the cars out of the crusher! A/C Thread
"as I ride with my a/c on... I have fond memories of sweaty oily saturdays and spewing R12 into the air. THANKS for all you do!

My drivers:
1987 190D 2.5Turbo
1987 560SL convertible
1987 190D 2.5-5SPEED!!!

1987 300TD
2005 Dodge Sprinter 2500 158"WB
1994GMC 2500 6.5Turbo truck... I had to put the ladder somewhere!