To stare about awkwardly.
1785. We see nobody, and do little else than sit in the chimney-corner, repeating over the same dull stories, or gawking at one another with sorry grimace.M. Cutler, Life, &c. (1888), ii. 2267. (N.E.D.)
1817. All with their wives, and some with their gawking offspring.Mass. Spy, April 2.