I would double check the tags on the left and right eyes. E.g. is there a “Left Blink” tag does differently to the “Right Blink” tag? I would go through every single node in the left and eye trees and check the tags carefully. (I assume you have the layer hierarchy the same for both eyes - hence tags is what I would check next.)
Character Animator auto-tags based on layer names, so if you had a spelling error in “Rihgt” for example, it might be auto tagging one eye but not the other.