Green’s Dictionary of Slang

1. (US) a fool.

1910		O. Johnson Varmint 39: ‘Why, Egghead, howdy-do?’ ‘Ah, there, Butsey White!’ ‘Ta-ta, Saphead.’.
1948		C.S. Montanye ‘Crepe for Suzette’ Thrilling Detective Oct. 🌐 You’re [...] trying to solve the thing yourself, to show what bright little boys newspaper guys are and what a lot of eggheads are cops.
1953		L. Uris Battle Cry (1964) 118: It isn’t funny, egghead.
1960		A Trocchi Cain’s Book 145: Fuck you, egghead!

2. a bald person.

1915		Sun (NY) 6 Dec. 9/6: What with [...] Nero Chink, Zulu Kid, the Dixie Kid [...] Egghead Ratty and London Smoke in pugilism.
1968		‘Hy Lit’ Hy Lit’s Unbelievable Dict. of Hip Words 13: egg head – Bald headed man, tell him to get a rug!
2000		N. Griffiths Grits 131: Yull be a fuckin egg-ed afurr tur thurty, so ye wull.
2004		Guardian G2 5 Oct. 27: Most eggheads don’t share my positive feelings.

3. a bald head.

1984		W.J. Caunitz One Police Plaza 88: Gino’s bald egghead seemed as shiny as ever.
1999		Guardian G2 10 June 5: Ffion Jenkins [...] fixes her lovely gaze on his funny little egghead.