Senior reserves were assigned to senior reserve commands. They were not assigned to units like Lay's Cavalry Regiment.
The man you describe might have been assigned to duty with a state militia company, depending on the law in Mississippi. In Alabama men up to age 60 could be required to render service in county militia units. These were local defense companies whose primary mission was preserving law and order at home. The need for this kind of service was far greater than most of us can imagine.