I've heard about mathematicians going through kind of the same thing when they get a weird proof that ends up being right from some weird source or themselves.

Which is fair, they get inundated with kooky proofs from amateurs all the time and odds are incredibly good that there's some major fatal flaw that the amateur doesn't see. Or in the case of themselves, there's a certain blindness that makes it a little more difficult to critically evaluate your own leaps. In ether case the way it manifests is by going over it many times and many ways, each time more certain that you missed something until you just kind of break. Only then do you publicly start suggesting that there might be something to this new leap.

> they get inundated with kooky proofs from amateurs

Source?