I tried to look at this a couple of ways, knowing that both show likely patterns, but not absolute certainty:
1: Using a full profile end of 2018 database, I checked the “last active” time value (*1):
hour nUsers %Users
0 77509 03,12%
1 78499 03,16%
2 81743 03,29%
3 84893 03,42%
4 87464 03,52%
5 89214 03,60%
6 95897 03,86%
7 104883 04,23%
8 108813 04,39%
9 115833 04,67%
10 114095 04,60%
11 122175 04,92%
12 125387 05,05%
13 122917 04,95%
14 127972 05,16%
15 126029 05,08%
16 124024 05,00%
17 120406 04,85%
18 110827 04,47%
19 106435 04,29%
20 98677 03,98%
21 102024 04,11%
22 81679 03,29%
23 73875 02,98%
Total 2481270 100,00%
I then delimited it to accounts that were exclusively last active during 2018 (to see if there was a difference):
hour nUsers %Users
0 33136 02,62%
1 34703 02,74%
2 37915 02,99%
3 40289 03,18%
4 42132 03,33%
5 42379 03,35%
6 45500 03,59%
7 51831 04,09%
8 57258 04,52%
9 63324 05,00%
10 60662 04,79%
11 66057 05,22%
12 64116 05,06%
13 65228 05,15%
14 68839 05,44%
15 68645 05,42%
16 70336 05,55%
17 68597 05,42%
18 59604 04,71%
19 56031 04,42%
20 50140 03,96%
21 46002 03,63%
22 38919 03,07%
23 34760 02,74%
Total 1266403 100,00%
2. Using the time from Merit TXs:
hour nUsers %Users
0 8693 02,90%
1 7736 02,58%
2 7572 02,52%
3 7823 02,61%
4 8165 02,72%
5 8573 02,86%
6 9435 03,14%
7 11410 03,80%
8 12911 04,30%
9 13139 04,38%
10 14383 04,79%
11 14152 04,72%
12 14515 04,84%
13 15314 05,10%
14 15916 05,30%
15 16427 05,47%
16 16381 05,46%
17 16130 05,38%
18 15886 05,29%
19 15602 05,20%
20 14490 04,83%
21 13432 04,48%
22 12147 04,05%
23 9858 03,29%
Total 300090 100,00%
All data seems to be UTC based (with no off-set). Crossing the above information, although not my preference for a concise taxative answer, I’d say that there’s a good chance that peak time is between 11 and 17 hours UTC, and with a rather equilibrated distribution that does not push one specific hour too far above others.
(*1): Not my ideal method, since the parser got a snapshot for every user at a different time, but could serve as an approximation.
(*2): This method is limited though, in the sense that only meriter data is considered (i.e. people who do not merit, merit seldom, or have little meriting power are not represented, or rather partially at best).