Green’s Dictionary of Slang

(US) the penis.

a.1900		‘Red Light Saloon’ in G. Logsdon Whorehouse Bells Were Ringing (1995) 76: She twisted my mustache, she smoothed down my hair; / My ‘ellick’ grew hard; it did, I declare.
a.1920		‘Joe Williams’ in G. Logsdon Whorehouse Bells Were Ringing (1995) 185: On Fifth Avenue I met a pretty lass, / I introduced her to my elick, and I shoved it up her ass.