On daytime watch changes I'd add a deck walk down / rigging / chaffing check unless you consider that a skippers only responsibility. Tethered of course. That also makes them more familiar with tethered work on deck.
Skipper does this on my boat at least twice a day --- usually first thing in the morning and once before the sun goes down...and unless it's really nice out I prefer people to stay in the cockpit unless there's a need to go forward.
If in shipping lanes, no distractions, no books etc. Constant scan (that's what watch means).
This, dear friends, is the value of AIS -- all the big fellas have it and show up on your plotter long before you see them. Most of your AIS "contacts" are never actually eyeballed because they're so far away. And the data that all boats send out takes the guess work out of "which way is he heading, how close will he come to us, etc." Fishing boats, however, are another matter -- many don't have AIS and so when in areas where fishers concentrate (e.g. Gulf of Maine), it is prudent to keep a much sharper watch.
At night, tethered no matter where you are. Especially if alone.
If more than one on watch, one is tethered at all times.
In general, I agree. But, every boat is different. On ours you can sit under the hard dodger forward of the wheel and be totally secure. The sides of the dodger and the wheel form a barrier that you need to work around to get out into the open behind the wheel. (The older I get, the harder it is to do this 10-15 times during a watch.) That's why our general rule is that you clip on before going aft of the wheel. General rules get modified as conditions change, of course.
Clean the cockpit at relief, no debris (some people need to be told that). On coming watch determines when it's clean enough.
Anyone who relieves themselves in my cockpit better clean it up!!!
The first act of the watch is to update the log,
The last act of the watch is to update the log.
I wan the guy coming on to know what's happened and so ask that they read the log and get a briefing before assuming the watch. The off going watch stander writes the log for the his watch.