from merry (adj.) + thought (n.)
The name alludes to the custom of two persons pulling the furcula of a fowl until it breaks; according to the popular notion, the one who gets the longer (in some districts, the shorter) piece will either be married sooner than the other, or will gain the fulfilment of any wish he may form at the moment.
From: Jack Hinton, The Guardsman
By Charles James Lever, Vol. I, 1849
Chapter II. The Irish Pocket. P. 12