found this on one of the "phrase derivation" sites....

"damn-my-eyes. adj. Naut. flashy; ostentatious. 1849 Melville 'White Jacket' 293 (ref. to 1843): You may put that man down for what man-of-war's men call a 'damn-my-eyes tar,' that is a humbug. And many damn-my-eyes humbugs there are. 1899 Boyd 'Shellback 16 (ref. to 1860's): A tall complexioned hat and a 'd--n my eyes' necktie."