Green’s Dictionary of Slang

(gay) one who performs anal intercourse.

1935		A.J. Pollock Und. Speaks 29/2: Dead eye dick, a jocker; sodomist.
1941		G. Legman ‘Lang. of Homosexuality’ Appendix VII in Henry Sex Variants.
1956		‘Eskimo Nell’ in ‘Count P. Vicarion’ Bawdy Ballads XIV: Now when Dead-Eye Dick and Mexico Pete go forth in search of fun, / It’s usually Dick who wields the prick and Mexico Pete the gun.
1965		Guild Dict. Homosexual Terms 11: deadeye dick (n.): A pedicator. (Slang.).
1979		Maledicta III:2 231: He also may or may not know the following words and expressions: [...] daub of the (tar) brush, Dead-Eye Dick, do it up brown [etc.].