What thermostat ? Dometic digital? Suburban?
Remember you MUST have 120VAC shore power to run the ceiling fan inside the A/C unit. It will NOT run on 12VDC alone. The furnace CAN run on 12VDC alone, but the fan setting MUST BE AUTO.
My Dometic had three fan settings : Auto, Lo, Hi
In heat mode, the correct setting is AUTO, and must have a 12 volt battery installed (strange but true or the furnace control board gets snippy, it likes a solid 12 vdc and the converter doesn't do smooth DC)
In Cool Mode, Lo, Hi, seemed to work, and must be on shore power (120VAC source). No 120VAC, NO A/C fans.
In Fan mode, Lo, Hi, and must have shore power (again 120VAC or no fan).