Yes sounds like the plan I would follow. But first look at the breaker with the 0 volts post. Check carefully for a small reset button. Most do not have a button, but some do so it's worth looking.
Next you could try disconnecting the wire from the 0 volt post. Give the breaker a minute to cool off and see if you now have 12.4 volts on both posts.
If yes then there is a short further downstream tripping the breaker.
If no then you have a bad breaker.
Another option that might yield some results is to plug in shore power or start the generator. Make sure to reconnect the 0 volt post if you disconnected it previously. If the 0 volt post now has power it tells you the converter/charger and fuses are all good back up to the suspect breaker. But you should be reading something like 13.6 volts on one post and 12.4 on the other post because the breaker is bad and isolating the two posts.
