Does a "dead" Elder get instantly revealed upon a showdown?

[StayPuft]

Again, I have not yet had a chance to re-read through the rulebook, so I apologize if this was answered there and I may have just missed it. As we all know, if an elder is "killed" during the course of the game (other than as result of a showdown with the villain) they are not removed from the game, but are simply turned a different direction to differentiate them from the Elders who are still alive.

This is because a "dead" Elder could turn out to secretly be an Evil Elder, thereby having faked their death and joining the villain. However, what I wasn't sure of... when the very first showdown begins after the Elder "died," do they get revealed instantly since they were "dead," or would they only be revealed if somebody accused them? In other words, it could be that, thematically, that hero didn't believe that they were really dead and believed that they were evil all along.