Answer: Called The Continental or the After-8, the fashion was first set by early movie star Douglas Fairbanks, and further propagated by top nightclub Latin bandleaders like Xavier Cugat. Other cinema stars like John Gilbert, Gilbert Roland and Ronald Colman followed, and soon every leading man needed a pencil thin moustache to look cool. Clark Gable’s moustache even had it’s own name- Sir Sharpness.
(from Tom Sito's excellent Blog)
I call mine "The Toff Tache" or "The Mod Wolf"