Your next step should be to write to the Arkansas Archives in Little Rock with a request for a lookup there. All of the archives of the southern states have the pension applications of the men and/or their widows in whichever state they happened to be living at the time of their application. In other words they did not have to travel back to the state of their service to apply for their pension. Your fellow served in Mississippi, but according to Jim Huffman's information, he must have moved on to another state, which seems to be Arkansas to you.