Green’s Dictionary of Slang

eggheaded adj.²

(US) bald.

1909		Sun (NY) 19 July 10/1: An eggheaded gentleman was dealing bank without a box.
1937		P. Gallico ‘Mine Eyes Have Seen the Glory’ in Brookhouser These Were Our Years (1959) 280: Curious egg-headed Humbert Fugazy, the little Italian banker.
1943		R. Chandler Lady in the Lake (1952) 89: The egg-headed clerk separated me from two dollars without even looking at me.
1977		G.F. Newman A Prisoner’s Tale 77: The eggheaded Donald Ludlow, who was in his mid-fifties, but looked older.