So, what type of evidence would it take to convince a FE proponent that he or she was incorrect? Is there any?
Cant be done. There are many posts with evidence that definitively disprove many aspects of flat earth nonsense on this forum, and when they turn up they are just plain ignored by the flattists. Examples include the disproof of their beloved bent light theory (flattist response: pretend nobody posted a disproof), the results of the Super Kamiokande neutrino experiments (flattist response: ignored and not commented on) the question of the actual location of the point we call the south pole on their disc (flattist response: ignored) and many others. These ignored threads quickly spiral down where people cant see them, until someone else chips in with the same idea.
The reason you cant convince them they are incorrect is because they all already know they are incorrect. This site is not about belief in a flat earth, none of them really believe it, its about honing debate and trolling skills to find an unbreakable argument. And when these unbreakable arguments appear, they are ignored or denied (a flattist will now post saying there have been no unbreakable RE arguments posted, which just proves my point, as anyone is able to go looking through the threads about the topics I mentioned.)