12.04 is probably below 50%. 12.24 is close to 50% but the instantaneous reading is probably a surface charge and will drift down over 24 hours even if disconnected. Just saying 12.24 is probably less charge than you think.
Real test would be a DC ammeter to know what is really going into the battery. Record the reading every 20 minutes for two hours.
But if you can get by on idling the truck one hour every three days, go for it. Likewise if you roll for a few hours most days you may not need a generator. If sitting still for an extended period is when the generator becomes more efficient.
If parked in decent sun 100w or 200w of solar could take the place of the gen. Probably less money and of course no gas can etc.
The 12 Volt Side of Life