Green’s Dictionary of Slang

gome n.

[gomer n.2 ]

(US campus) a devotedly hard worker.

[US]L. Birnbach Official Preppie Hbk 90: 13 Words For The Person Who Is Working — 1. Grind 2. Squid 3. Pencil Geek 4. Cereb 5. Grub 6. Weenie 7. Throat 8. Tool 9. Wonk 10. Gome 11. Nerd 12. Spider 13. Conch.
[US]W. Safire What’s The Good Word? 300: At some southern colleges [excessively hard workers] are ‘gomes’ [...] The derivation of this word undoubtedly comes from ‘Gomer’ as in ‘Gomer Pyle.’.