This is a much better picture of your ancestor's service than you had earlier. For example. we now know that he participated in not one but two major battles in 1862. His record can be divided as follows --

Jun 08 1861 - Company enrolls in state service, Capt Parker's Company, Marietta MS
Aug 16 1861 - Company enrolls in CSA service. In camp at Iuka MS as Co "G", 26th Miss Regt
Dec 03 1861 - To Bowling Green KY, then to Fort Donelson via Russellville KY
Feb 16 1862 - Escape from Fort Donelson to Nashville TN and then home.
Apr 02 1862 - Survivors form Co K, 32nd Miss Regt - Corinth and Tupelo MS, then to Chattanooga via Mobile and Atlanta. March over Cumberland Mtns to Kentucky. Battle of Perryville KY
Dec 26 1862 - Left sick at Wartrace TN, early stages of Murfreesboro Campaign
Jan 10 1863 - Former members of 26th Miss Regt with 32nd Miss ordered back to their original companies.

Undetermined period after Dec 26 1862
Possibly captured by Federal forces at Wartrace. If so he would be sent to prison camp and exchanged about Apr 1863. Confederate prisoners taken during the Murfreesboro Campaign were released by Federal authorities at City Point VA on the James River. If healthy and able to travel, they were sent home on furlough for sixty days. While at home your ancestor would have learned that he had been ordered back to the 26th Mississippi. This would account for his absence during the first six months of 1863 and perhaps longer.

May 05 1864 - Battle of the Wilderness and subsequent actions with the 26th Mississippi with the ANVa.
Apr 02 1865 - Capture at Hatcher's Run VA and sent to prison
Jun 28 1865 - Release on oath at Point Lookout MD and subsequent travel home

Regarding members of the 26th Mississippi who survived Fort Donelson being assigned to the 32nd Mississippi, see the following (request of Gen Johnston mentioning 300 members of the 26th Mississippi not captured at Fort Donelson).
http://www.mississippiscv.org/MS_Units/32nd_MS_Inf.htm

Two closing remarks --

Yesterday morning you wrote, "I'm not sure about the origins of the 'homemade gun' comment." I'm guessing that you were responding to my earlier reference to home manufacture. Home manufacture means items built in factories located in Southern states, the South being home. "Homemade" brings to mind something put together from parts in a shed back of the house. I don't believe that's what either of us meant.

As for Jinkins working as a saddler, evidently you meant that he would've been more valuable to the Confederate war effort in his civilian occupation. Normal cavalry duties would not have included saddle manfacture. But since Jinkins volunteered, he was setting aside his civilian occupation. Also, bear in mind that at the time of his enlistment very few cavalry companies existed. At the end of 1861, the State of Mississippi had produced perhaps two dozen mounted companies; maybe less. There were far fewer than that in the summer of 1861, so the opportunity to enlist in a cavalry company being recruited in his home county probably didn't exist.

Suggest you check manufacture of revolvers in Texas during the war, compare that to the total number of Confederate and state troops in Texas, then decide how these scarce resources would been been apportioned. Enlisted men in Texas state commands would be at or near the bottom of the supply chain.