Southgate is a 1960s subdivision of ranch homes and small villas south of the base, close to the Southgate shopping area. Much of the ductwork is original, and original duct in a Florida house has usually lost some of its insulation and some of its seal. A system that heats unevenly here is often a distribution question rather than a furnace fault.
The housing stock is mostly concrete block on a slab, with one air handler in a hallway closet or the corner of a garage. Returns in that layout are short and the supply trunk runs through the attic, so a run that has come apart above the ceiling shows up as a single cold bedroom rather than a system that has failed outright. Flex duct from the same period also sags between hangers, and a sagging run loses airflow well before it splits.
The neighbourhood sits between Siesta Drive, US 41 and Bee Ridge Road, close enough to the water that outdoor equipment collects salt, and sheltered enough by mature trees that the cabinet stays damp on the shaded side. A heat pump here runs in cooling mode most of the year, so heating faults tend to be found during a cooling call: a reversing valve that will not switch over, a defrost board that has stopped, or auxiliary heat that has never been tested.