Rules FAQ

Event card effects engage the game state at the time they resolve. If an event card creates a lasting effect on a set of cards, only cards that are in play at the time the event card is played are eligible to be affected. Cards that enter play after the resolution of the event are not affected by its lasting effect.

So Dragon Sight affects characters that are eligible (participating, in-play, non-Dragon) when it's played. Nothing changes after that, if another characters jumps into play or loses the Dragon trait, etc.