Green’s Dictionary of Slang

in excellent condition, usu. of a bull or a pimp; intensified as rum ti tum with the chill off.

1823		Egan Grose’s Classical Dict. of the Vulgar Tongue n.p.: Rumtitum. Synonymous with prime twig; in fine order or condition. A flash term for a game bull.
1835		G. Kent Modern Flash Dict. 29: Rum ti tum with the chill off – good, slap up, the tippy, excellent.
1841		‘F.L.G.’ Swell’s Night Guide K4: Rum-ti-Tum, excellent.
1885		Bulletin (Sydney) 16 May 9/3: Miss Juno was last heard of from Maryborough (Q.), where she was playing in a new piece – ‘The Bonnie Wishwife.’ Rum-ti-tum-tum.