Speaking about a mechanical switch, such as the ball valve in a water / fuel / gas pipe, do you expect to have "on" / "off" or "open" / "closed" states?
That is: if you put labels in each position, would they read: "on" and "off", or: "open" and "closed" (or any)?
While the valve that the switch operates may be 'open' or 'closed' to allow the flow of liquid or gas, the switch itself is more likely to be referred to as being on or off.
For example, most British houses have a stop valve in them - a single tap that isolates the water supply to the whole building. Using this tap is idiomatically referred to as "turning the water off".
You mention "a mechanical switch, such as the ball valve", but a switch and a valve are two different things. A valve is usually "open" or "closed" (rather than "on" or "off"), and Google Books seems to corroborate that:
It also gets more results for a switch being "open" or "closed", but searching the Google Books corpus for "the switch is open" suggests that the vast majority of those are for electrical circuits. I'd say that if you wanted to indicate the position of the switch itself, then you could say "on" or "off", but if you wanted to refer to the flow of a fluid, then "open" or "closed" might be a better choice. I recommend asking about a more specific situation if there's one in particular that you're interested in.
