Dan Milner's Songs of England, Ireland & Scotland, A Bonnie Bunch of Roses (Oak Publications, 1983), page 181, has the following:

Heather on the Moor

Here's a bouncy song Robin Morton collected from Hugh Lees of Enniskillen, Co. Fermanagh. Paul Brady was always being asked to sing this one when he lived in New York.

Source: R. Morton, Folksongs Sung in Ulster.
Recording: Paul Brady, The Gathering, Green Hays 705.

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(text as linked in the DT above)

The first DT tune (HTHRMOOR) is the one that is given in the book.

~ Becky in Tucson