The house is 63 years old. Yes, the "Open Ground" duplex outlet was identified with a three prong plug-in outlet tester, before I opened it up. Inside there are only two sets of two wires for the two outlets; the wires are cloth and rubber covered. There is no ground wire
63 years old, 1962... I imagine the branch circuit wiring is cloth covered NM, Romex. Though going from memory, the two conductor where insulated with TW thermal plastic, PVC insulation.
It is possible, because of local Fire Codes, Electrical Codes, AHJ (Authority Having Jurisdiction) in your city required houses back then to be wired using BX, steel armored cable. (In 1962 the steel armor was not used as an equipment grounding conductor,) In 1962 it may have still had cloth covered rubber insulation covering the bare conductors.
Yes, the "Open Ground" duplex outlet was identified with a three prong plug-in outlet tester, before I opened it up. Inside there are only two sets of two wires for the two outlets;
That indicates a convenience outlet branch circuit. More than likely a 15A circuit. The outlet terminals were used for feed through in and out circuit through the box. Good chance there are several wall outlets, and possibly ceiling lights on the circuit.
Shut off the breaker at the panel and check what is dead. Identify with a piece of tape or a post-it at each dead wall outlet.
Turn back on the breaker and check the wall outlets for a ground with your plug-in tester. Upstream, (toward the electrical panel), from the one for your audio equipment may show there is a ground. Down stream will show an Open Ground.
If it is BX don’t assume the integrity of the safety equipment ground. Good chance it will fail in the event of a Hot to ground fault event. Back in 1962 there were not any 120V 15A or 20A 3 wire grounding type outlets. They were only 2 wire.