the first two verses are similar lyrics to those recorded by Joan Baez and Gene Foreman -

I like the tune of the Baez version and I was taught a guitar accompaniament for it, but it always seems to short and bare to me and I was looking for verses to flush it out. Does anyone know more about the origin of the song (before Hans Theesink's version); where did Joan Baez get the song from?

When you hear them cuckoos hollerin' (3x)
It'a a sign of rain, buddy, it's a sign of rain.

Goin' up on a mountain for to see my baby (3x)
And I ain't comin' home, buddy, and I ain't comin' home

When you hear them hoot owls callin' (3x)
Someone's dying, whoa-oh, someone's dying

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found something here, Monica Grabin added some verses http://www.monicagrabin.com/?section=music-156

    A folk song from the American south, where Cuckoos are sometimes called "rain birds" for their supposed tendency to call before a storm. I felt the song needed more verses that were actually about birds, so I wrote the ones about Mourning Doves and Crows.

    When you hear them Cuckoos hollering,
    When you hear them Cuckoos hollering,
    When you hear them Cuckoos hollering,
    It's a sign of rain, buddy, it's a sign of rain.

    When you hear them Screech Owls calling, (3X)
    Somebody's dying in the world, somebody's dying.

    Going up on the mountain, for to see my baby, (3X)
    And I ain't coming home, buddy, I ain't coming home.

    When you hear them Mourning Doves moaning, (3X)
    It makes you feel like crying, buddy, makes you feel like crying.

    When you hear them black Crows squalling, (3X)
    There's a Hawk nearby, buddy, there's a hawk nearby.   

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Joan Baez: https://www.youtube.com/watch?v=epoMnWLeE68