Empirically it seems that I just gained tag wiki edit suggestion privileges (ability to add a suggestion to the review queue, not to get my changes approved without peer review) in Stack Overflow when my reputation got over 500 points. However, this old answer suggests there is a completely different logic involved, but it doesn't seem to match my personal experience. As far as I can tell the current logic is not explained in the FAQ or on SO's own privileges help page, although there is a lot of content in both and I might have missed something.
I did see somewhere a note that anyone can suggest edits to the tag wikis, but I've misplaced where that was (somewhere within the linked FAQ pages, possibly?), and at least personally I couldn't suggest tag wiki edits in SO last week when my reputation was 495. I assume that this could be one of the many cases where SO does things a bit differently than most sites, but if so, is the limit in SO truly 500 reputation or some other milestone that I happened to hit over the weekend?
Edit: there was no 'Edit tag info' button at all when I tried on Friday, but now there is.