Thanks for the information, your right about the limitation of researching this unit. My GGGG-father and brothers join this origination when it was formed. Then a few of his brothers went on and joined other units that fought at Vicksburg (46th INF and 1st Lt Arty).
I have reviewed other postings on this site, and have come to the conclusion that the 2nd was a local-militia-type unit (task: homeland/State defense).
If you run across any information and/or anyone, who can enlighten me of the 2nd, or 1st Lt Arty would be great.