Red Eyes are one of the pursuers that appear on the 5th Floor after Viola picks up the doll head from one of the cabinets in the medicine room.
They have the appearance of large, even human-size, bloodshot eyes with red sclera and black irises.
The Witch's House
If these pursuers touch Viola, she will turn red and it immediately cuts to the game over screen, making it how exactly she got killed somewhat ambiguous.
If Viola stays in the room she escapes in for too long, they break the door down, and kill her. Upon leaving the room, the player will see that the Red Eyes increased in number. To avoid them, it is suggested that the player picks up the doll head from the left, then loop around to the top of the room and towards the entrance.
The eyes are likely canon to the fact that Ellen had gouged them out of her own being before switching bodies with Viola, to make her 'despair as she died'. (Information found and attributed to the Secret Ending.)