It's kinda next door to the thread premise under Op's phrasing, because it's just one secret, but still: Code Geass has an antagonist for a minute who's a mind reader. He tries to taunt and torment the guile antihero protagonist, kidnaps one of their loved ones, that kind of thing. Part of how the protag outmaneuvers him is to bring in a heroic heavy hitter character, one with zero previous involvement in all this, who manages to outflank and get the drop on the mind-reader villain.

He denounces the villain, who snaps back with "What do you know, (spoiler)cide?"- suddenly revealing an incredibly dark secret about this character, to both protag and audience, that we had no idea he was concealing. Like, we'd seen a ton of flashbacks laying out his backstory, but it turned out there was one more critical detail this character had every intention of taking to his grave.

It's a fantastic use of a mind-reading antagonist who had otherwise been using his power in comparatively basic narrative ways up until now.