Green’s Dictionary of Slang

squash n.

[SE squash, the vegetable]

1. (US campus, also squash-head, squashie, squashy) a fool; thus squash-headed adj., foolish.

[US]H.L. Williams N.-Y. After Dark 37: Look here, girl, don’t you get up your back against me – I ain’t a country squash to stand any of your slack!
[US]W.C. Gore Student Sl. in Cohen (1997) 12: squash n. A foolish, ‘soft’ fellow.
[US]M.G. Hayden ‘Terms Of Disparagement’ in DN IV:iii 201: squash, a vacillating person. ‘I say you are a squash, but I hardly think you have that much backbone.’.
[SA]A. La Guma Walk in the Night (1968) 52: He reached for his bottle of cheap wine. [...] ‘You better go slow on that,’ the girl, Nancy, said. ‘I can take it,’ Willieboy said thickly. ‘What do you think I am? A squashie?’ [Ibid.] 75: Blerry young squashy, Michael Adonis thought [...] For what’s he got to act like a blerry godfather?
[US]C. Cooper Jr ‘Yet Princes Follow’ in Black! (1996) 255: What squash-head took a fifty-dollar play on one-a slip! What-a squash-head!
[US]‘Tom Pendleton’ Iron Orchard (1967) 14: Big squash-headed sonofabitch thinks he owns the place.

2. (US) the head, face.

[US]J. Weidman I Can Get It For You Wholesale 59: All you had to do was take one look at his squash to see that he believed it.
[US]Goldin et al. DAUL 206/1: Squash. (New England) The face; the head.
[US]B. Rodgers Queens’ Vernacular 144: out of one’s squash very drunk, high or mad. [Ibid.] 188: squash (fr black sl) head, by extension brains.
[US]T. Wolfe Bonfire of the Vanities 290: Guy’s so hung over, he’s bleeding into his squash.