Generally, an applicant was eligible for a pension only if he was indigent or disabled.

You can procure his pension papers through a service provided by these message boards, see:
http://history-sites.com/research/

They may provide insight into the rejection of his pension. I am guessing that he was neither disabled nor indigent.

The article in the Confederate Veteran Magazine ought to provide further insight. Unfortunately, that Volume is not available on-line, nor do I have it in my files.

…..

J Watt Tinkler

Residence was not listed;
Enlisted as a Private (date unknown).
He also had service in:
"A" Co. TX 5th Cavalry
Other Information:
died in 1924
After the War he lived in Houston, TX

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

** Confederate Veteran: v. 33, p. 187

….

J. W. Tinkler, age 19, Private, Capt. John S. Shropshire’s Company, 5th Regiment Texas Mounted Vols.* enlisted August 17, 1861 at Columbus, Texas by J. S. Shropshire for the war, captured in New Mexico during the campaign of 1862, paroled at Fort Union, New Mexico, April 5, 1862, admitted General Hospital, Franklin, Texas June 12, 1862, Rubeolae (Measles), discharged June 26, “left without permission,” paroled July 3, 1865 at Columbus, Texas

* This company was successively designated as Captain Shropshire’s Company, Captain Wells’ Company and Company A, 5th Regiment Texas Cavalry

M323: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Texas