A taylor’s goose; a smoothing iron used to press down the seams, for which purpose it must be heated: hence it is a jocular saying, that a taylor, be he ever so poor, is always sure to have a goose at his fire. He cannot say boh to a goose; a saying of a bashful or sheepish fellow.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
Goodyer’s Pig * Goose RidingNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes