Green’s Dictionary of Slang

(US black) a flashy automobile sporting ostentatious tailfins and as such the choice of pimps; e.g. a 48-59 Cadillac, or a Chevrolet 49 Cabstar; thus the tailfin itself.

1949		Dan Burley ‘Back Door Stuff’ 29 Jan. [synd. col.] Some of the more brazen playboys are getting their fishtails painted white and buying up a lot of white suits.
1957		W.R. Burnett Underdog 58: A big, two-door fishtail whizzed past just behind him.
1995		B. Short (con. 1949) Saloon Singer 110: They drove a 1949 black convertible Cadillac with fishtails and red leather upholstery.