After my faux pas in mistaking Henry for Harrison I did some digging in Ancestry. Harrison, his wife Unity and 8 children appear in census records for 1850 - 1880. Harrison and Unity were married in North Carolina in 1841. Their first recorded child, John was born later that year and the last, Elizabeth was born in 1864. Military records are consistent with what has already been posted in this thread.
Death records show Unity died on 4 April 1895. Details concerning Unity's death were noted as being provided by her husband, Harrison Kallam, so he was alive as of that date. I found Harrison's Find A Grave link at Chestnut Knob Cemetery in Ridgeway. His date of death on the site is listed as Dec. 1880, which would seem to be in error. The only family member linked to him is daughter Mary W. Kallam Clark. I find no record of Harrison after 1895.