Well a fully charged 12v battery should measure about 12.6 volts unloaded varying slightly with ambient temperature.....clearly you have a bad or shorted battery. When you mentioned green I assumed you meant the Ford chassis battery charge sight button showed green......which is usually a visual indication of a fully charged condition.
When you replace your chassis battery make sure with your voltmeter that the coach charging systems (shore power converter and engine alternator) are each doing their job to keep the new battery charged. Good luck.
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