How often and in what context are Doctor Eckleburg's eyes mentioned in chapter 2 of The Great Gatsby?

The second chapter of F. Scott Fitzgerald’s novel The Great Gatsby opens with a vivid description of a small industrial strip along the road between West Egg and East Egg. Anyone taking the train to New York passes through this grimy landscape. Nick calls this place the “valley of ashes” because it is inhabited by “ash-gray men” and “gray cars.”
Overlooking this desolation is an old faded advertisement for the office of Doctor T. J. Eckleburg, apparently an optometrist in the borough of Queens. The sign is weathered and out of date, but it impacts the narrator powerfully. Look at how Nick describes the sign in the opening paragraphs of chapter 2:

The eyes of Doctor T. J. Eckleburg are blue and gigantic—their irises are one yard high. They look out of no face, but, instead, from a pair of enormous yellow spectacles which pass over a nonexistent nose . . . But his eyes, dimmed a little by many paintless days, under sun and rain, brood on over the solemn dumping ground.

This poignant description of the sign is echoed twice later in the chapter when the sign is described as watching over the people in the valley. Nick walks along the road “under Doctor Eckleburg’s persistent stare,” and Tom exchanges “a frown with Doctor Eckleburg.” This repetition tells the reader that this sign is important and that they should pay attention to references to Doctor T.J. Eckleburg’s eyes throughout the remainder of the story.