Next mention of "Rio Grande" is in

1879        Adams, Captain R.C. _On Board the Rocket_. Boston: D. Lothrop & Co.

Sea captain Adams was son of the earlier mentioned N. Adams. This account refers to his days on U.S. barque Rocket, circa 1865-1869 -- it was just before the time described by his dad. Adams has a section in which, from a 1879 vantage, he is talks generally about shanties they sang some 10 or more years earlier.

The third set of working songs comprises those used at the pumps, capstan and windlass, where continuous force is applied, instead of the pulls at intervals, as when hauling on ropes. Many of the second set of songs are used on such occasions, but there are a few peculiar to this use and of such are the following:

RIO GRANDE.

I'm bound away this very day.
    Ch: Oh, you Rio!
I'm bound away this very day, I'm bound for the Rio Grande.
    Chorus: And away you Rio! Oh, you Rio!
    I'm bound away this very day, I'm bound for the Rio Grande.