By the very fact that your ancestor is listed on the CWSS and Ancestry.Com, it means that there IS a record of this man in the form of a Compiled Military Service Record. It may be short, as many Trans-Mississippi CMSR's are; however, something does exist. You just can't tell until someone actually pulls the record/microfilm; how much information is available. I have just mailed a grouping of Confederate service records for soldiers from Alabama, Louisiana and Texas. One of the files included over forty (40) cards in the soldier's packet, another included only two (2).
I might ask, has anyone on the Texas message board looked at the microfilm of Gidding's Battalion? What was the general quality and quantity of these records? According to the NARA microfilm index, Gidding's Battalion occupies 1-1/2 microfilm rolls and includes records for 619 men. Honestly, that's no too bad for a Trans-Mississippi (West of the Mississippi River) Confederate battalion. Finally, the fact that he has an alternate name designation (i.e., J. A. Alvis and James Alvis), indicates that he "should" have at least three (3) cards in his packet, including the packet envelope itself.