Mike,
Brownsville Station was located about a mile east of Lonoke on US Highway 70. The camp of the Third Michigan was located in what is currently a soy bean field just east of the City Ball Park which is just east of the National Guard Armory.
Where the Ball Park now stands was the site of some sort of military engagement as it was literally covered up with fired bullets.
It was called Brownsville Station as it was on the Little Rock to Devalls Bluff Railroad and was the debarkation point for Brownsville two miles to the north.