Nobody can doubt that a "mountain jack" is a lumberjack's tool used for the purpose indicated.

But beyond that, a "mountain jack" is an old term - still in use evidently - in parts of West Virginia for a fox squirrel and in parts of Pennsylvania for a snowshoe hare.

Since I've never heard a squirrel or a rabbit "holler," I'm inclined to think the MJ in the song is a narrow-gauge locomotive of the kind
sometimes used in Appalachian lumbering operations.

That term has also been around for a long time.