A Voltmeter, is not a battery monitor.
reading 12.2 volts under a 5 amp load is much different than 12.2 volts rested, not having seen a load or charging source for several hours.
Ciggy plugs are horrible connectors. The ciggy receptacles are usually very underwired, and if there are other loads on this circuit, as there often are, then the voltage reading will be low.
If you want a Voltmeter, then voltage at the battery terminals itself will yield a more accurate reading than anywhere else.