Link was nearly given eye-beams during the development The Legend of Zelda: The Wind Waker on the Gamecube console, according to Nintendo development staff.
In an Iwata Asks interview that discusses the upcoming HD remake of The Wind Waker for Wii U, the original game’s design manager, Satoru Takizawa, mentions that due to The Wind Waker’s stylized, almost anime-esque art style with large eyes, eye beams were considered as one of the features that would take advantage of the new look.
“Now that the eyes had gotten much larger, we wanted to make [the characters’] facial expressions richer by increasing the number of patterns for the eyes and mouth,” Takizawa says. “Partway through, we even talked about having beams come out of those eyes!”
Takizawa elaborates, “[Shigeru] Miyamoto-san and [Takashi] Tezuka-san said we needed to supply a reason for the eyes being so big. I don’t think beams were really an option, though.”
Ultimately, instead of giving Link eye beams, the decision was made to have Link’s large eyes convey hints to the player, by having them move and gaze at important places and objects.