The linguist John Sinclair points out that the usage of eye vs. eyes does not overlap very much. In other words, the plural for the eyes in the body, but the singular is rarely one eye, but is used rather in a series of conventional phrases:
an eye for an eye
an eye for detail
with an eye toward ...
a keen eye
a good eye
keep your eye on the ball
So to understand eye as merely the singular form of the noun eyes is to misunderstand basic Engish usage. When the singular eye is used for the anatomical eye, then it is usually in the context of disability or injury.
This kind of linguistic fact does not come out in dictionaries, typically, but rather through the study of large corpora of actual linguistic usage.