Akin to George Wallace's "pointy-headed intellectuals", but with a different metaphorical shape. Eggheads are people who "think too much"; the term was coined in the 1952 US presidential campaign, to describe (bald) Democratic nominee Governor Adlai Stevenson - a smart, eloquent patrician, especially compared to the adman-created "Common Man" persona of his opponent, General Dwight Eisenhower. Ike was, at the time, president of Columbia University, IIRC, and no slouch at thinking.