Green’s Dictionary of Slang

(UK Und.) a bull kept for baiting.

1823		Egan Grose’s Classical Dict. of the Vulgar Tongue n.p.: rumtitum A flash term for a game bull: one that is kept on purpose to be baited: and to try the courage of the dogs.
1825		Pierce Egan’s Life in London 19 June 164/3: The New-Subscription Rum-te-tum will be out to-morrow' within six miles of town, when a Valuable Silver Collar will be given to the Best Dog that is entered.
1831		‘Gallery of 140 Comicalities’ Bell’s Life in London 24 June 4/4: John Bull and Bill Gibbon’s Bull. There arnt been such a rumtitum out for many a day.