Second hand disappears on watch.

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I would imagine an always on, second hand sweeping the screen all day, would greatly reduce battery life and require the watch to be charged more often. The always on display is intended to provide the time (perhaps not by the second) when you're not using the watch, without adversely effecting the duration of an all day charge.

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FWIW, I usually used Siri for timing pulse and respiratory rates, and which had the added benefit of avoiding touching my Watch. (A consideration that might be less of a factor in your environment, but possibly workable for you, too. And still hands-free.)

Second hand will not show with always on.

You would need to wake the watch for it to show.