It was Norman Kennedy, as above 4-5 posts, who used the Ricky-doo-dum words and tune to The Overgate. I believe Jeanie Robertson sang both choruses, the "Roving Eye" one I adduce above [also sung by Robin Hall & Jimmy McGregor], & the ricky-doo-dah one; with tunes not identical.
The ricky one is most associated, IMO, with The Keach In The Creel; to a tune sometimes slightly varying from that in DT linked above by Matthew Edwards.

~M~