Green’s Dictionary of Slang

1. one who tosses up coins in a gambling game based on guessing heads or tails.

1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc.
1828		G. Smeeton Doings in London 39: This fellow is one of the greatest Gaffers in the country. When he hides a halfpenny, and a flat cries ‘head’ for £10, a ‘tail’ is sure to turn up.
1831		Satirist (London) 20 Nov. 262/1: This fellow is one of the greatest gaffers in the country. When he hides a halfpenny, and a flat cries ‘Head’ for 10l., a ‘tail’ is sure to turn up. One of his modes of commanding the turn-up is this:—He has a halfpenny with two heads, and a halfpenny with two tails [etc].
1911		L. Stone Jonah 215: The spinner tossed the coins again, and, as they fell, the gaffers cried, ‘Two heads!’.

2. the ‘straight’ front man for any form of fraud or marginal business.

1973

G.V. Higgins Digger’s Game (1981) 29: We got ourselves a fine, fat gaffer in this guy.