Looking at the locations of the users with high reputations (which tend to include a lot of people who answer), and filling in those whose locations I know but who don't give one here, it looks like a little bit more than half the number come from the USA, Canada, and other countries that have similar time zones. The rest cover Europe (including UK), Russia, India, Australia, New Zealand, and many other places around the world.
There's almost always some people active.
Purely anecdotally, there are relatively more answerers active when the North Americans are either at work or after work -- but at the same time, there are more people asking as well, so it's also easier for a question to disappear off the front page.
Less anecdotally, there's a number of relevant data queries at data.stackexchange.com
has pretty strict criteria$^\dagger$ but you might be able to modify it to suit your needs; it looks for when accepted answers that score more than 50 from users with more than 10000 reputation were posted (a very high bar, few users answers regularly satisfy all of those criteria, so you're mostly looking at posts from a small subset of good answerers). In any case, that suggests that UTC 12-22 may be somewhat better than UTC 1-8 with other times in between.
$^\dagger$ Only 4.7% (!) of answers were counted in those figures. Probably the biggest factor in what gets included is the 50 score limit on the post (that limit is more likely to be hit if a question is asked an answered when North America is active -- it can be somewhat harder to get upvotes on good answers at other times), with the 10K rep not far behind. I think both are too strict, cutting out a host of really good answerers.
Note that the criteria above would have also suggested that you wouldn't have the best chance to get a good answer right when I am posting this. There may be a lesson in that, also.
Looking at some other queries, the three high rep users with the most accepted answers* will answer questions asked at any time -- in each case the times questions are posted which they answered are almost uniformly spread by time of day -- with a mild peak when people post more -- irrespective of when those answerers are active.
* (the only ones I checked but I expect that pattern will hold up for many more)
(Why? because while they don't answer around the clock, when they are answering, the most-accepted answerers scroll back through the questions until they hit questions they've already seen; if you want to get the attention of our most prolific producers of accepted answers, it really doesn't much matter when you post)