"fool, simpleton," 1825, perhaps from gawp (v.) "to yawn, gape" (as in astonishment), which is attested from 1680s, a dialectal survival of galp (c. 1300), which is related to yelp or gape and perhaps confused with or influenced by gawk.
gave
gavel
gavotte
gawk
gawky
gawp
gay
gaydar
gayety
Gaylord
Gaza