Green’s Dictionary of Slang

pointy-head n.

[both senses are derog. and suggest that an excess or an absence of brain lead to a ‘pointed’ head]

1. (US) a fool.

[[US]N. Algren Chicago: City On the Make 88: Joe Felso doesn’t trouble his pointy little head].
[Aus]R.G. Barrett White Shoes 73: I’d like to lay a big shit on each one of your pointy little hayseed Australian heads.
[Aus]M.B. ‘Chopper’ Read How to Shoot Friends 208: I’m tired of explaining to these pointyheads.
[UK]Observer 1 Feb. 33/4: We should miss [...] pieces such as last week’s attack on former colleague, [...] whom he described a ‘pointy head’ and a ‘Mekon’.

2. (Aus.) by stereotype of sense 1, a peasant.

[Aus]P. Temple Black Tide (2012) [ebook] She got in the family way, one of the local pointies [...] Good blokes, but you wouldn’t breed from them.
[Aus]P. Temple Black Tide (2012) [ebook] We’ll just freewheel down there, lights out, pray some pointy in a truck doesn’t come along.

3. an intellectual; the implication is that they have no practical abilities [the locus classicus occurred in a speech by the far-right Alabama governor George Wallace in 1972].

G. Wallace in Hamill Irrational Ravings 311: Some pointy-head who can’t park a bicycle straight. They all come from the multimillion-dollar tax-exempt foundations.
[US]N.Y. Times Mag. 12 Mar. 106: He [i.e. George Wallace] told those people they were being screwed by pointy-heads in Washington and New York.
[Aus]Age (Melbourne) 10 Apr. 29/1: The ‘network shiny-bum pointyheads’ as Steve Vizard once referred to them [i.e. TV executives].