I remember that song and I've been trying to track it down. As I recall, it was recored by The Mills Brothers, circa 1968. I always thought it was Gin Town Road, but I haven't been able to find any reference to that.

Here's the verse I remember:

Hey Luther, wave to Brother Griffin
He's smilin' and he's headin' this way
He's been checking out the girl
On the Gin Town Road today
He says it's his moral duty
To see that she ain't doing no wrong
But that was early this mornin'
I wonder why he's been gone so long...