Origin of the "white feather as a symbol of cowardice"

The OED uses Grose's dictionary as its first source and adds

1. A white feather as a symbol of cowardice. [...]With allusion to the fact that a white feather in a game bird's tail was considered a mark of inferior breeding.

1785 F. Grose Classical Dict. Vulgar Tongue White feather, he has a white feather, he is a coward, an allusion to a game cock, where having a white feather, is a proof he is not of the true game breed.

Grose's example, game cock/breed is a use of "game" in the hunting sense and OED game, adj. 1. Of a person or animal: full of pluck, spirit, or fight; spirited, plucky; intrepid. Also applied to actions, attributes, etc.