(Archaic) an old countrywoman; orig. late 16th century, probably a contraction of godmother, says the dictionary, but why not ‘grandmother’? Seems related to ‘gaffer’.
‘… laughed at the greybeards and gammers who said that they had seen him flying it the sky in their younger days.’
Source: JRR Tolkien, The Hobbit (London: HarperCollins, 1995), p. 176