The image of running goes back to the first spirituals collected. Higginson collected one, "Down in the Valley,"first verse:

We'll run and never tire (3x)
Jesus set poor sinners free
Way down in the valley,
Who will rise and go with me?
You've heern talk of Jesus,
Who set poor sinners free.

Run, Sinner, Run
1st verse (from N. I. White, American Negro Folk-Songs)
Run, sinner, run, yo' house on fire, (2X)
Den my little soul goin' to shine home (2x)

Combine with the songs about who is going and who is not, naming relatives and members of the congregation:

I Got a Mother
(third verse (from N. I. White; similar collected by Work in 1907))

I'se gotter brotha in the promised land,
I'se ask muh brotha does he wanta go long,
If he don't wanta go, I'll journey on
To the promised land.

The ideas are combined in the old spiritual style by Rev. Temple.

Also reminiscent of:
If the seeker won't go, I'll journey on (3x)
I'm on my way, God knows I'm on my way.