I heard this on the Cumberland Highlanders Show on RFD-TV last year. I didn’t recognize it but my husband said it’s a common old British saw. I don’t remember the group who sang it in the Bluegrass version but the Wikipedia link says the song is quite common in Bluegrass music. Here it is, h/t to Maggie’s Farm, which showcased it today and jogged my memory. http://www.maggiesfarm.anotherdotcom.com
https://en.wikipedia.org/wiki/My_Grandfather%27s_Clock
Music and lyrics by Henry Work, arrangement and performance by Tom Roush, who has this work, a lesser-known sequel and other works available on a CD, http://tomroush.us
I find it very charming.