"Off" indicates an open circuit for household applicances, lights, etc

I think the use of "OFF" in this context predates modern electronics. Alarm clocks go off, ships sound off their horns, etc. (though the phrase "noises off" is from a completely different root ). It may come from "Go Off"="Explode"="Noise" perhaps?

And B96, rather like my telling every one my Mother's maiden name, we now know to bring a set of little metal disks to avoid setting the alarms off when we burgle (sorry - burglarize for you us'ns) your house

Rod