Green’s Dictionary of Slang

(US Und.) a detective.

1919		C.H. Darling Jargon Book 11: Eagle Eye—A detective.
1927		Clark & Eubank Lockstep and Corridor 173: Eagle-eye—detective.
1934		B. Appel Brain Guy (1937) 68: Suppose some eagle eye had spotted McMann’s license number? [Ibid.] 130: We ride downtown in the hocked car [...] afraid of every cop who might be Eagle-Eye Gus.