Green’s Dictionary of Slang

intellectual, or posing as such.

1901		Houston Daily Post (TX) 13 June 4/5: These egg-headed imbeciles who go about slaying the objects of their affection.
1919		W. Deeping Second Youth n.p.: A little egg-headed pedant [R].
1939		R. Chandler Big Sleep 82: You’re crazy, you godam egg-headed — !
1991		W.T. Vollmann Whores for Gloria 37: The television also showed the big eggheaded politicians.
1999		Guardian Guide 20–26 Nov. 69: A bushel of egg-headed eclipse watchers.