This is the only Rumley I find in Confederate Army records

Fred C. Rumley
Enlisted on 8/1/1861 as a Corporal.
On 8/1/1861 he mustered into "I" Co. AL 24th Infantry
* Oath Allegiance 5/6/1865 (place not stated)
died 3/18/1924 in York, AL
(Died at age 79 years)

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records
- Confederate Veteran Magazine

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Fred C. Rumley, Private, Company I, 24th Alabama Infantry, enlisted October 18, 1861 at Mobile, Ala. by Maj. Goodwin for 12 months, promoted 4th Corporal December 15, 1862, admitted Way Hospital, Meridian, Miss, February 15, 1865, gunshot wound, captured by 1st Brigade, 2nd Cavalry Division, USA,, April, 1865

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama

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RUMLEY-- Died at York, Ala., on March 18, 1924, Fred Rumley, Company I, 24th Alabama Volunteer Regiment. He enlisted August 1, 1861, and was honorably discharged May 6, 1863. His age was seventy-nine years.

Confederate Veteran: v. 32, p. 316.