I used to be obsessed with the perfect time to post on Facebook, but then I realized how much Facebook has changed over the years. As opposed to twitter which shows you tweets in chronological order Facebook shows you the posts in order of how much you will enjoy them.
From a business perspective that means if I post 10 things one right after the other each post will be shown to people that may be interested in it, so few people will actually see all the posts and most of those people won’t see it when it actually gets posted. So I won’t say that timing is totally irrelevant on Facebook but I’d say that it is worth testing every hour of he day, even extreme off peak hours to see how posts do.
Also, you may want to consider posting things when a few of your best people are online, that way they will see it and be engaged, while no one else is on, and it will do better because they were all engaged with the post. It is basically impossible to test this unless you can find a time when your best 1% are on and no one else is.
Do you find that certain times of the day are better for posting?