1958 Cessna 182A on the original "Rotating Beacon" circuit there is what appears to be a small motor on the lower right firewall just above the copilots' rudder pedals that turns on when the circuit is activated. There is a newer separate circuit for a "Belly Beacon" that activates the red beacon light on the aircraft.

Confused as to what this is or why it remains in the aircraft. The current theory is that it is possibly a DC-AC inverter that used to power an AC rotating beacon that is no longer installed but the previous owner was not interested in removing the entire system when it was upgraded/replaced?

Some of the old stuff can be confusing. There where two solutions back in the day for making differing voltages or things like AC. There was a collective term of Dynamotor for them. They used a small motor to turn an equally small generator or alternator to make whatever voltage you wanted or flavor of electricity needed. So if you disconnect it and nothing changes, it is simply a relic of electronics/electrics past. You would need to do a 337 to remove it, or, if there was a 337 removing the old AC beacon, then just simply remove it.

Old military aircraft where full of these things, whining and failing right and left. Personally I think them to be hazardous, since they had a tendency to smoke check when they ended their lives.

It's a noise filter for your radio, or for a previous radio that has been removed. It keeps generator whine out of the radio. you can buy one on E-bay right now for $65.00 plus shipping.