Speaking from the other side of the equation, as someone who used to look for and post interesting freebies in the Deals forum, I can tell you anecdotally that I paid considerably more attention to the KDP Select exclusive-or-else slushpile on days when I had more relative leisure time (i.e., not on new-release Tuesdays or the 1st of each month or on Mondays when a guaranteed slew of religious and business freebies trickled in every week and where after posting about a dozen new listings/updates, I really
didn't have much remaining inclination to trawl for the backlist/indie stuff).
So going from that, I'd say that good times to freebie are when people have the spare time to casually browse on the internet in order to see your book in the first place, and also the corresponding extra free time to decide whether it's interesting enough to 1-click or not based on the blurb/sample.
Based on this, I suggest trying holidays/holiday aftermath long weekends, and Sundays. Friday is not too bad (end of work/school week when the load tends to lighten up a bit; people want to relax a bit before gearing up for the weekend), but it, like Saturday, tend to be days when people tend to have other entertainment plans scheduled which may not involve surfing the internet.
Also, if you've got a blog/other website presence, pre-announce your freebie well in advance and post a reminder on the day it's free as well. I can't tell you how many times I idly went to a site on a holiday to see if they were having a sale or not, and lo and behold, they were, completely without any indication before the very day or announcement other than on the website frontpage.
For what do I subscribe to the newsletters for again, if they're not going to bother to use them to send out actual useful news?!