Green’s Dictionary of Slang

staring, esp. by a man at a woman.

1846		C.P. Hodgson Reminiscences of Aus. 302: This day’s work [climbing a tree to look around] is what is generally though not elegantly termed ‘eye-balling.’.
1965		D. Pearce Cool Hand Luke (1967) 13: Eyeballing is punishable by being put in the Box.
1972		Milner & Milner Black Players 204: In some towns in Tennessee where I grew up [...] You could get yourslf in jail for indiscriminate eyeballing.
1989		H. Harrison Bill [...] on the Planet of Robot Slaves (1991) 118: So – when all the eyeballing is done, you get to tell me what you are doing here.
1991		B. Hamper Rivethead (1992) 79: Her cleavage tumblin’ out of her shrunken smock, her legs all stacked up for maximum eyeballin’.
2007		N. McCall Them (2008) 91: White girls, off limits. No eyeballin, greetin, embracin [...] or otherwise touchin the fruit.