Green’s Dictionary of Slang

(US) in earnest, sincerely, straightforwardly, honestly.

1896		H. Blossom Checkers 36: Say, on the dead, I’m glad to see you.
1900		A.H. Lewis ‘Politics’ in Sandburrs 96: On d’ dead! I was farmer enough to t’ink I’d t’ank him for bein’ me guide.
1906		S. Ford Shorty McCabe 198: On the dead now, I don’t care so much about loomin’ up in the picture.
1914		Wash. Post 28 June 6/6: But, say, my picture, on the dead, / Ain’t been in any pape.
1960, 1975		Wentworth & Flexner DAS.