T. J. Eckelberg is not a character in The Great Gatsby. Rather, the faceless eyes of Doctor T. J. Eckelberg loom at the characters from a billboard for an oculist. The aging billboard is located in the valley of ashes and depicts the large bespeckled blue eyes of Eckelberg. Fitzgerald suggests that this symbol has meaning for the characters, but he never comes right out and tells the reader what that meaning is. To Nick, the eyes seem to be judging the characters and American society in general.
There may be something godlike about these eyes. After the death of his wife, George Wilson makes a clear comparison to these eyes to those of God. To him, they are the eyes of God, who sees everything that people do and judges them for it. With God's eyes staring out from an advertisement, Fitzgerald may be suggesting that America has replaced religion with capitalism.
The eyes of T. J. Eckelberg may also remind the reader to view the characters from an impassioned distance. Too often they are caught up in their own machinations to see clearly what they are doing. Even Nick is too involved in the events of this story to be a completely reliable narrator. However, if we view the events of the book and the people in it as if we were eyes on a billboard, we might just get a more accurate picture of what is actually going on.