Different cultures would probably make different choices for the "singular" day.
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I would make the case for Christmas in our culture because almost everything shuts down on that day so the trouble of “Who is on call on day X?” is minimized. Other cultures would pick a different day but that leads to the problem of it being Monday in your zone and Tuesday in their zone between your days.
See
https://www.crystalinks.com/dayoutoftime.html
for the version of it in the calendar I mentioned.