Characterized by staring, gaping, or displaying a foolish or vacant expression; somewhat awkward or dopey.
From 'gaw' (to stare) plus the productive English suffix '-ish' meaning 'somewhat like'; likely influenced by parallel formation with 'gawky' and 'gawp'.
The '-ish' suffix is one of English's most creative tools—you can attach it to almost anything to mean 'somewhat like,' and gawish shows how speakers invented descriptive words by following these ancient morphological patterns, even for obscure concepts.
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