Ken, this is just a stab. Unfortunatley, each house is as different as the parade of tradesmen who have been through there.
I don't think it's possible for it to have functioned while connected to two different circuits. If there is no sign of heat damage (blackened parts), then it should be OK. If it were causing a problem, it should constantly trip the breaker.
I see stuff that is totally inexplicable, yet, has been there for 40 years w/o issue. When that's the case, I install the new stuff just the way the old stuff was connected. No one has ever called back or sued me to replace their burned out home.
Do you think it may have ever had two on/off switches in separate locations? If it is a separate circuit, is it dead and out of the system, or still live?