I don't believe Henry Harrison Alexander to be related to this Thomas Alexander. There are two Thomas Alexanders This Thomas, born in 1795 (died 1838) and another Thomas born in 1799 (died 1858)
1850 Census for Clay County Indiana has a Thomas Alexander, aged 50 (born 1799) with Mary Alexander, age 38 and the following children:
George - 18
Calvin - 14
Lewis - 12
Mary - 9
John - 7
Alexander - 5
Alexander - 3
Laura - 0
Reference: pgs. 31-32 of 1850 Federal census - Indiana: Clark and Clay Counties (NARA Series M432, Roll 138)
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:S3HT-D14Q-NKH?cc=1401638&am... : 9 April 2016), Indiana > Clay > Washington > image 31 of 45; citing NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
The Thomas born in 1795 died in 1838 and is buried in Symmes, Edgar County, Illinois
https://www.findagrave.com/memorial/19387984
Would love additional insights as there is much confusion between the families of the two men. I have done a DNA test through familytreeDNA to help sort things out. I cross-listed the results to GEDmatch as well (T436566).
Wondering if these men are cousins... but haven't found a link... yet!