You can find John T. Shrader Civil War Record at: https://www.fold3.com/browse/21/h_BQBoX3gzZJS3qf4A8fArOOVl6IZz_bd (this just let me know that his info is there)
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Dear Mr. Shrader,
Thank you for posting your request on History Hub!
We searched the Arlington National Cemetery Explorer for John T. Shrader without success. Then, we searched Find-a-Grave and located an entry for John T Shrader who was buried in Arlington National Cemetery in Section 13, Site 6916. We searched the Arlington National Cemetery Explorer again using the section and grave number information and located a grave for JT Shrader of West Virginia.
We also searched the National Archives Catalog and located the series Carded Records Showing Military Service of Soldiers Who Fought in Volunteer Organizations During the American Civil War in the Records of the Adjutant General's Office, 1762 - 1917 (Record Group 94) that includes two service records for "Shrader, John T." from West Virginian units. Both records have been digitized and may be accessed online using the Catalog. It is not clear if these records are for two different soldiers or for one soldier that enlisted first in one organization and then joined a separate organization. The muster out date for the earlier record was one day before the enlistment date for the latter record, which allows for the possibility that both records are for the same person who transferred from one unit to another.
We also searched the National Park Services’ Civil War Soldiers and Sailors System and located two entries for West Virginia soldiers named John T. Shrader.
Because he served in a West Virginia unit, there may be additional records concerning his service in the custody of the West Virginia State Archives.
We hope this is helpful. Best of luck with your research!