Green’s Dictionary of Slang

1. of a man, to have sexual intercourse; thus well-thumbed girl, a worn-out prostitute.

1890–1904

Farmer & Henley Sl. and Its Analogues.

2. (Aus.) to dismiss, to send along.

1960

J. Brosnan Long Season 54: The clubhouse man [...] stands at the door with a list. He may smile halfheartedly if he liked you, or he may just thumb you on your way.

3. (Irish) of a woman, to masturbate.

1997

Irish Times 9 May n.p.: The accused agreed he had told the gardaí he had no interest in women but he was incorrectly recorded as adding ‘I always let them thumb themselves’ [BS].