>>4482901 (lb)
I was thinking about this some more, and can be a little clearer about why the coincidence is interesting.
(a) "10 days darkness" and "EO Jan 1" are two of the most prominent topics out there, so putting these on the table is a restricted set for finding statistical correlations. The EO date is known, the mystery is the interval of the 10 days of darkness.
(b) One of the very few clues Q gave us about "10 days darkness" was the word "shutdown", which could very naturally be interpreted as a federal govt shutdown (perhaps the most common use of that word when discussing the federal govt). So even without any other evidence, it would be reasonable to suspect that "10 days darkness" might begin at the start of a federal govt shutdown. This is an "a priori" theory that's been floating around out there.
(c) There was a govt shutdown starting Dec 21. If that's the start of 10 days darkness, the period extends to Dec 31. (Yes, I'm sidestepping here the thorny computer science index question of "do you count the first day, e.g. is the first item 0 or 1?")
(d) There are two low-probability clues that appear consistent with this specific timeline. Q's initial post about 10 days darkness being at 12:31 am, a coincidence with 12/31 being a special date (1:360 odds); and the EO going into effect Jan 1 the very next day (if random, there's no particular reason to think this would be 10 days [of darkness?] + 1 after a federal govt shutdown begins.)
Q could have arranged for these three events to line up this way, so it would fit the way Q gives us "coincidences" and clues.
Contrary considerations: There's a leap here in interpreting the EO on Jan 1 as "light" to contrast with the "darkness" (this is playing off the darkness to light meme.) So pulling the EO into this discussion might be not well supported, unless the EO plays a more important role than I can see right now. (Expanding the pool of available judges is important, but doesn't seem this important.)