With the recent free trial availability of the Ancestry.com records for the 1890 Union Veterans Census, I was able to locate the listing for acting master Samuel Eakins, who had commanded the ALLIGATOR, for a short while. He mentions this fact in the census record, and notes the vessel as being a sub. torpedo, which I assume is either a "submarine" or "submersible" torpedo. At the time of the census, Eakins was living in Raleigh, North Carolina. Tried to find out more from the census records, but nothing has been found, so far.
Mark Ragan's volume indicates that not much was known about Eakins, and he seems to have just disappeared from the history books, after his initial involvement with the ALLIGATOR.