The character with this trait has an eyepatch. He or she doesn't necessarily have to be blind in that eye, only requirement is that the character wears it enough to be associated with it.
An eyepatch is a small patch that is worn in front of one eye. It may be a cloth patch attached around the head by an elastic band or by a string, or an adhesive bandage. It is often worn by people to cover a lost or injured eye, but it also has a therapeutic use in children for the treatment of amblyopia.