Green’s Dictionary of Slang

(US) cheeky, impudent.

1876		St Louis Globe-Democrat 19 Jan. n.p.: Others of the crowd think the bar-keeper is a ‘funny boy’, and that his remarks are ‘too thin,’ ‘too gauzy,’ and ‘won’t wash’.
1879		F.W. Benteen letter 3 May in Carroll Camp Talk (1983) 128: ‘Little J. chews tobacco.’ He’s a gauzy man to me.