Green’s Dictionary of Slang

Timbucktoo n.

[the perceived distance]

a euph. for SE hell; usu. in phr. go to Timbucktoo.

[US]W. Winchell On Broadway 15 Apr. [synd. col.] Mummy told Daddy to go to Timbuctoo and Daddy told Mummy to go some place else.
[US] ‘Old Zebra Dun’ in G. Logsdon Whorehouse Bells Were Ringing (1995) 83: All you so and so’s, you said this hawse was tame! / Well, I’ll ride him! I’m his owner! But I’m takin’ care of you. / You boys now have a burro! You can go to Timbucktoo!