I've just had a look at the Bodleian for the broadsides of Burns' Farewell and the 4 copies there all start Adieu, a heart-warm fond adieu, which is the start of The Farewell To the Brethren of St. James' Lodge, Tarbolton, 1786 (ie the Masons), the tune to which is Goodnight and Joy Be Wi' You A', so that's probably the tune required.

I'll post a set in a few minutes.

Mick