What does "to skin your eyes for sth" mean?

The expression in question occurs in the following passage from Moby-Dick

“It’s a white whale, I say,” resumed Ahab, as he threw down the topmaul: “a white whale. Skin your eyes for him, men; look sharp for white water; if ye see but a bubble, sing out.”

I get from the context that it may mean to actively look for something, to look for it with a substantial effort. I did some research, yet I have found no confirmation of my implied understanding of to skin your eyes for something. Am I not correctly implying the meaning of it? What do y’all think the phrase means in this passage? Do you know of any helpful reference?