The "unblinking eyes" are fixated on her. They see her deteriorate and do nothing about it. They can read her soul and basically are witnessing all that she is going through. The eyes represent her status: A person to be seen and not heard. Someone who is put in a room, deprived of all the things that she needs to make a good recovery but whose condition is so misunderstood by a man-dominated society that all she can do is be literally "caged" by staying in a room all day, deprived of communication.
Therefore the symbolic significance of the author seeing unblinking eyes lies in the fact that she feels like some form of fish inside a tank, or like a caged bird with he eyes of the world on her, but doing nothing to help her condition
In "The Yellow Wallpaper," the "absured, unblinking eyes" might represent the lack of agency that women had in the late 19th century. The narrator in the story thinks that she sees eyes on her at all times. Similarly, she is under her husband's scrutiny during every moment of her life. The narrator claims that he has labeled her as "hysterical" and has therefore locked her in the attic room. The narrator's husband John has restricted any sense of agency that the narrator might have otherwise, and in order to control her, he convinces her that she is truly ill. Even when John is not physically in the room, his presence is still there, hence the "unblinking eyes."