Shawn; Your fella is the 1st MSM Cav vet, primary proof via censu and pension records as below, link through daughter Katie Rosanna Hoover See unsourced story end of posting for migration history.
Jacob Ayers Hoover
Father: Henry Mann Hoover
Mother: Rachel Nichols
Birth Date: 30 Jan 1842
City: Wayne
County: Zanesville Muskingum
State: OH
Marriage Virginia Adeline Hoyl b: 4 NOV 1842 in Henry Co., Missouri, (age 8/1850 Census, Dade Co., MO)
1920 census
Name: Jacob R Hoover Sr.
Spouse: Virginia A Daughter Katie R.
Birth: abt 1843 - Ohio
Residence: 1920 - Phillipsburg, Phillips, Kansas
1910 census
Name: Jacob A Hoover
Spouse: Virginia
Birth: abt 1842 - Ohio
Residence: 1910 - Phillipsburg, Phillips, Kansas
1905 Kansas State Census
Name: Jacob Hoover Senior
Birth: abt 1842 - Ohio
Residence: 1 Mar 1905 - Arcade, Phillips, Kansas
1880 census
Name: Jacob A. Hoover
Spouse: Virginia A.
Birth: abt 1842 - Ohio
Residence: 1880 - Salem, Daviess, Missouri
1870 census
Name: Jacob Hoover
Birth: abt 1840 - Ohio
Residence: 1870 - Grand River, Daviess, Missouri
Civil War Pension Record Kansas
Jacob A Hoover Re Helples Child Katy R. Hoover
Co B 1st Mo S.M. Cav
May 22 1918 App# 655?74 Certificate 431484
April 11 1920 App# 1666.453 Cert# A-L-?3-30
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Name: Henry Mann Hoover , Jr.
Birth: 19 JUL 1817 in Muskingum Co., OH
Death: 1870 in Coffey, Daviess Co., MO
Burial: OCT 1870 Coffey, Daviess Co., MO
Migrated to MO in 1846 settled in Gallitin Twp.
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Name: Virginia Adeline HOYLE
Birth: 4 Nov 1842 in Henry Co,Mo
Death: 26 Nov 1928 in Phillips Co,Kansas
Father: Solomon HOYLE b: ABT 1785 in Virginia
Mother: Elvira DAMEWOOD b: 1813 in Tenn.
Marriage 1 Francis HORN
Children
Mary Francis ( Molly) HORN
Marriage 2 Jacob Ayers HOOVER Sr
Married: 12 Apr 1864 in Henry Co,Mo
Children
George Henry HOOVER b: 14 Feb 1865 in Daviess Co,Mo
William Comador ( Pum) HOOVER b: 14 Sep 1866 in Daviess Co,Mo
Diken ( Dicken) HOOVER b: 29 Jul 1868 in Daviess Co,Mo
Hernado Courtes ( Nando) HOOVER b: 16 Aug 1869 in Daviess Co,Mo
Henry Mann HOOVER b: 20 Oct 1871 in Daviess Co,Mo
Jacob Ayers ( Jake) HOOVER b: 20 Oct 1873 in Daviess Co,Mo
Katie Rosana HOOVER b: 20 Aug 1876 in Daviess Co,Mo
Don Carlos HOOVER b: 21 Nov 1878 in Daviess Co,Mo
May Belle HOOVER b: 15 Dec 1880 in Daviess Co,Mo
Edward HOOVER b: 9 Nov 1883 in Daviess Co,Mo
Unsourced story via Jennie H. Lassen
Virginia and Jacob homesteaded in KS 1876, making the trip from Phillips Co. Ks. to MO many times in the years to improve on the land. Many drought years and bands of indians made it almost unbearable. It was called a tree claim. They would go each year or so, plant the trees, apple, cherry, plum, all kinds of berries, bushes and cotton woods. In 1884 the trees were getting fairly big and grandpa built a sod house, out buildings and a Blackmith shop, where grandpa worked at his trade. Being close to Highway 36, 4 1/2 miles east from the county seat of Phillipsburg. Grandpa had all the work he could handle with area farmers and travelers. In 1900 they built a large frame house, grain storage buildings and a new barn. It was a very fine and lovely farm.
Virginia never learned to read by herself but she could quote scripture from the Bible and was an ardent christian. Jacob being more tolerant. Jacob was a well read person for his time, had a beautiful hand for writing and kept records. A truly honest man. He stood over 6 feet and was a lean well built man. Virginia was a tiny person in build, feminine and very spirited. Her hair was dark in younger days.