Bright morning star's a-rising,
Bright morning star's a-rising,
Bright morning star's a-rising,
Day is a breaking in my soul.

There is a certain amount of religious literacy to connect these dots but this song has strong Epiphany themes (the church season that follows Advent/Christmas). This is a church holiday that Shakers would not celebrate so I very much doubt their involvement.

I don't know enough about Moravian theology to say much more than this: Moravian influences on American Indians through Moravian missions in the Carolinas and elsewhere make the possible American Indian connection intriguing and believable. Moravians certainly celebrate Epiphany religiously.