Unless Carado's are very different than other Roadtrek/Hymer, the inverter will draw 100 watts of power from the batteries when turned on even with nothing else running. If you are plugged into shore power, it will charge the batteries if you have the batteries on.
Voltage is only an accurate measure of depth of charge with no load either charging or discharging. For instance, my refrigerator kicking in usually knocks a couple tenths off the voltage that come back as soon as it stops running.
That 13.4 reading is probably the charger. If I am parked in the sun with my solar panel I usually have a 13.1 reading. The 12.4 reading may indicate depth of charge if nothing else is on. But that is still only a rough estimate. You really need to not only turn everything off but let it rest overnight or longer to get a completely accurate reading.
Voltage is at best a rough indicator of the depth of charge. BTW, for AGM batteries I think 12.4 is less than 75%. You would expect 12.6 at 75% with 12.8+ fully charged and 12.3 at 50%. The voltages are a little different than standard flooded lead acid batteries. If you are concerned about precision, you might want to check with the battery manufacturer. Frankly, given all the uncertainties of voltage I don't worry about it. If you are over 12 volts you are probably OK, but the closer you get to that point the harder it is on the battery.