If there is not a smart alternator fitted, then it looks like there is a fault with the charging from the alternator. 12.4V is not by any stretch of the imagination a fully charged battery. Measure both the cab battery voltage and the hab battery voltage when the engine has been stopped for more than an hour, preferably while it's dark to avoid confusion from the solar panel contribution. Then start the engine and measure the cab voltage again, while the engine is running. The voltage should jump to over 13V, ideally more like 14.4V. That means the alternator is charging the cab battery. If it doesn't increase, then you have a charging problem.He said a reading of 12.4 was a full battery not under charge.
Also measure the hab battery while the engine is running. The voltage should be similar, ie between 13V and 14.5V. That will tell you that the split charge relay is working OK or not.
Are you in a position to hook up mains power, so that the mains charger can charge the batteries? You should get similar results for the voltages. Note that the voltage while charging does not indicate the state of charge of the batteries. It takes a few hours of charge to bring them up to 100% from 12.4V.
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