Gaze

Red eye is a "Gaze". Look away.

A Gaze attack usually applies a status effect such as Petrification which turns you to stone, preventing you from moving, turning or using actions and abilities.

It's often followed by another attack that takes advantage of it.

You can avoid the Gaze by turning away from the enemy when you see a red eye shining from the enemy.

Gaze can also be avoided by having the Blind debuff inflicted on yourself.