Green’s Dictionary of Slang

taffy-tugger n.

also taffy-puller
[tug one’s taffy under tug v.]

a masturbator.

[US]AllAboutSex.org 🌐 ‘Words for Masturbation’ [...] 339. Taffy pulling contest. 340. Taffy tugger.
L. Fritz In Nine Kinds of Pain [ebook] Dallas is pathetic and probably couldn’t get hard enough [...] Dallas is just a taffy-puller.