I had this posted under "What Is It" and got it positively i.d.'ed as a Signature Ink Stamp. Found in Vicksburg area. Can't help but wonder who owned this and what letters or documents it was affixed to during the campaign for Vicksburg.
Nice find. There should be a small threaded hole in one end that held a thumb screw which tightened to hold the individual letters that made up the soldier's name. Sutlers had the stamps and typeset letters and would custom make these for soldiers.