Possibly this question depends on location. I'm most interested in the US convention.
I have read here a convincing claim about sink faucet handles: when there are separate hot and cold handles, cross handles (knobs) should always turn on counter-clockwise, but lever handles which are off pointing outward should turn on by pulling them toward you: that's counter-clockwise on for the left, hot handle, but clockwise on for the right, cold handle.
What about a double lever handle for a shower, where the two handles, which are wall-mounted, are pointing outward and might turn either up or down?
Here, you are generally standing looking down at the handles. Is down on, which would be counter-clockwise for the left/hot handle and clockwise for the right/cold handle, matching the sink configuration? Or is up on, which has the same feeling of "pull toward you" but is actually opposite in terms of the direction of rotation?