Thomas said "this is why you will not locate their parents."
I think what he really meant to say was that you may not be able to locate his parents by using easy to find online records such as census records starting with 1850, since by that time Terrell was already married and living on his own.
Since your profile lists you as a member of Ancestry for 8 years, I assume that you are beyond searching the "easy" stuff for this man.
I did find a reference (with no sources given) that listed Terl's birth as 6 January 1826 in Grayson County, Virginia and his death as 16 July 1897, Clay County, Indiana. If you did not have this death date, then it may help in finding an obit or death record in Indiana.
It appears that several Tipton families moved from Grayson County to Estill, then some of Bath County KY 1830-1840.
I also found index entries (1890-1895) for Pension Office correspondence (on FamilySearch) showing that Terl was making an attempt to have his charge of desertion removed from his Civil War record. If you can get the actual correspondence, it might prove interesting.
Your find-a-grave entry mentions only company F, but it was Company F of the 22nd Kentucky Infantry (Union). However, I checked this unit looking for possible brothers, etc. and Terl was the only Tipton listed.
I wish I could help more, but unfortunately I'm too far away.
Good luck with your search.