eye See you!
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In the context of the Great Gatsby there are many links between the moon and the Dr. T.J. Eckleburg billboard.  Fitzgerald seems to use many differences and comparisons very discretely when writing about the moon and the billboard. Here are some examples of how the moon and billboard share some common links:

 
The moon looks over the Earth as the billboard looks over the Valley of Ashes and the characters of The Great Gatsby.

 
The eyes on the billboard are described as "pale and enormous," just like the moon, and also as "gigantic".  Later in the novel Fitzgerald describes the eyes of Dr. T.J. Eckleburg as passing "over a non-existent nose."  We often tend to picture a face on the moon which is truly not existent.

 
Fitzgerald talks about the billboard as having "peculiar intensity from less than 20 feet away."....sometimes the moon is so bright that it seems as though we can reach up and grab it.

 
Fitzgerald also seems to use a lot of the same words to describe the moon and the billboard: "their faces were touching except for a pale thin ray of moonlight inbetween".  He also uses the adjective pale to describe the enormous eyes of the billboard.  This also leads to imaging the eyes as being two big pale moons.  

 
The moon is then described as lusterless.  Fitzgerald makes another comparison when he says that the eyes of the billboard are "dimmed by paintless days under sun and rain."  This leads us to picture in our mind two spheres that are both very pale.

 
Though the moon seems similar to the billboard through the physical descriptions, it seems to be the complete opposite of it through the relationships in The Great Gatsby:  When Gatsby is going to kiss Daisy, the moon was lighting up the sidewalk, but when Wilson sees the billboard he knows that it sees all, and he associates it with God.  He realizes that Myrtle can hide her affair from him, but not from God, realizing the reality of their situation and marriage can not be denied. The billboard seems to be the realistic point of view, while the moon is the dreamer, which goes along with the idea of romanticism.  Nick cannot have Daisy but goes to extremes.  Nick leaves Gatsby "standing there in the moonlight" because he wanted to wait there until Daisy goes to bed.  Fitzgerald describes the moon in scenes of Gatsby's parties.  The entire time Gatsby was trying to win Daisy's love with his lavish parties and wealth.  Therefore that is why the moon is always in the setting when Gatsby and Daisy are together because it is Gatsby's dream but it is not reality.  

Cristina Knopfhart