What does "fast eye" mean?
Solution 1:
The meaning is most likely from this definition of fast:
a : wild
b : sexually promiscuous
From Wiktionary:
Having an extravagant lifestyle or immoral habits [from 18th c.]
And from Etymonline:
The sense of "living an unrestrained life" (usually of women) is from 1746 (fast living is from 1745).
Without delving too far into literary criticism, the preacher's daughter, Sabbath Lily, is often the victim of men in the novel and is later revealed to be a nymphomaniac. So this sense of the word is undoubtedly what was implied.