The importance of this question is related to an incredibly significant motif in this story, which is that of blindness. The narrator again and again comments on the way in which so many characters avoid seeing the reality and truth that is in front of them and embark on elaborate ways of remaining in a state of blindness. From the blond man at the beginning of the story who doesn't truly "see" the narrator to the boys in the battle royal wearing blindfolds, blindness is a key motif that indicates the inability of those affected to see what their prejudice prevents them from seeing.
Light therefore, especially at the beginning of the story where we see the narrator living after experiencing an epiphany about both himself and the struggle for civil rights, is a key symbol of self-knowledge and understanding. The narrator, as he tells us, has finally understood that he is a character who, in many ways, does not exist because the prejudice of others around him will not allow him to be seen as a real human person. It is therefore ironic that he chooses to live in such light as a representation of his struggle to remind himself that he does exist and that he is real.