This song doesn't appear to be in the DT. It was recorded by Joan Baez 1964 and Cindy Mangsen (1980s).
Does anybody know of its origin, and does anybody know of any additional verses other than the following .....

(Chorus) When you hear them Cuckoos hollerin' ..... It's a sign of rain, buddy its a sign of rain
I'm goin' up on the mountain, for to see my baby ..... and I ain't comin' home, no I ain't comin' home
When you hear, that hoot owl callin' ..... somebody's dying, somebody's gone.

I'd love to hear of its source in the tradition, along with more verses, if possible.