Smartphones were whipped out to figure out what the tune refers to, but we couldn't zero in on it.
Patrick Wamsley has found a blog on hiking a site by that name, and here's a relevant quote:
Habbie's Howe is the setting for much of Allan Ramsay's 'Gentle Shepherd', and there is an excerpt from it carved into a stone panel 200m or so  from the bottom of the steps. It refers to the 'flowerie howm' on the opposite bank, as well as features such as Peggy's Pool with its waterfall. Look out for Sandy Cave .