Green’s Dictionary of Slang

(US) of a stare, cold, chilly; also as adv., in a chilly manner.

1960		(con. 1930s) R. Barber Night They Raided Minsky’s (1968) 270: Jack [...] gets a dead-eye bead on him.
1978		R. Price Ladies’ Man (1985) 41: She stared at me deadeye.
2004		N. ‘Razor’ Smith A Few Kind Words and a Loaded Gun 168: I gave him the dead-eyed stare that I normally reserved for screws.
2009		Financial Times Weekend Mag. 10–11 Jan. 41/3: They are hard to hit – small and with a fast, weaving flight. You need to be a dead-eye Dick and then some.