Frank and Ken,
Bryan's Battn. was officially the "1st Battalion, Cherokee Partisan Rangers." It comprised five companies that were consolidated with several companies of Watie's 1st Cherokee Regt. to form the "2nd Cherokee Mounted Volunteers" on Feb. 3, 1863. The newly formed regt. was commanded by Col. William P. Adair. I have probably seen a half dozen variations to the name of Bryan's Battn. including the one you mentioned. Most variations surface in pension applications filed by the Arkansas white boys that served indian units under Bryan and Adair. As many recruits came from Washington Co. as Benton Co. A few also came from the other border counties of Ark. with the IT.
Bryan later commanded the "Cherokee Regiment for Special Services" that was formed in the later part of 64 and 1st half of 65.
S. S. Gramham is likely Seabron S. Graham that Ken noted. He was enlisted about 7-1-62 for 3 years by Capt. John Miller in Benton Co. He was paid on 9-30-1862. He appears as "Present" on a 2nd Cher. Regt. muster roll for the period 10-1-62 to 6-30-63. There are no service records after July 1863.
Hope this helps a little.
Hugh Keen