a line or strap passing across the forehead and attached to a pack on the back thus aiding the burden bearer.
— From a later note defining a word in a record dated 4th Sept. 1759, in Transactions and collections of the American Antiquarian Society, v. 11, "Manuscript Records of the French and Indian War", 1909, p. 230 (see note at bottom of page).
The earliest attestations given in OED are 1855 for the verb and 1860 for the noun, but as the example from the American Antiquarian Society and examples from other secondary sources show, the words were in use with this sense at least a hundred years earlier (1775, 1781).
John Russell Bartlett's 1848 Dictionary of Americanisms (the 1860 edition is cited in OED to attest both the verb and the noun) says the origin of 'to tump' is probably "an Indian word":
TO TUMP. Probably an Indian word. It means to draw a deer or other animal home through the woods, after he has been killed. Ex. 'We tumped the deer to our cabin.' Used in Maine.
TUMPLINE. A strap placed across the forehead to assist a man in carrying a pack on his back. Used in Maine, where the custom was borrowed from the Indians.
What was the now obscure linguistic origin of 'to tump' and so also 'tumpline'?