I'm Wandering To and Fro is in the Cooper edition of the Sacred Harp and has been reprinted in An Eclectic Harmony. Attribution is Author unknown but copyright 1907 by W.M. Cooper

I don't know the original song referenced but it may be the texts more than the tunes that are related.

Here are the correct words.
It starts with just 2 part female voices:

I'm wand'ring to and fro,
In this wide world of woe,
Where streams of sorrow flow,
And then I'm going home.

4 part chorus: We' camp a while in the wilderness,
We' camp a while in the wilderness,
We' camp a while in the wilderness,
And then we're going home

v.2 (women)
And when my faith is tried,
In Him I will confide,
And all the storms out ride,
And then I'm going home.

(chorus all)

Notes: An Eclectic Harmony is a book of @100 tunes 4 shape books other than the 1991 revision of the Sacred Harp. It's becoming very popular as a supplement for use at socials & 'alternative' sessions.