R G. Hamill enlisted as a Private in Company D, 37th Mississippi Infantry May 1, 1862 at Chock Agency, recorded on the May 7, 1862 muster roll held at Columbus, Mississippi, with remarks "Furloughed from May 1 to 15," his status is not listed on the next bi-monthly muster roll for the period May & June 1862 nor the following
[Comment, he drops off the radar, this is unusual, had he not been present at the next muster, his status, dropped, discharged, deserted, etc., would have been noted]

M269: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi

37th Regiment, Mississippi Infantry

37th Infantry Regiment was organized during the spring of 1862 with men recruited in the counties of Clarke, Lowndes, Greene, De Soto, Jasper, and Claiborne. After participating in numerous battles in Mississippi the unit was assigned to General Hebert's Brigade in the Department of Mississippi and East Louisiana. It was captured when Vicksburg fell and during the siege it lost 17 killed, 56 wounded, and 7 missing. Exchanged, the regiment contained 26 officers and 442 men in December, 1863. It then served under Generals Mackall, Cantey, and Featherston in the Army of Tennessee. The 37th fought in the Atlanta Campaign, endured Hood's winter operations in Tennessee, and ended the war in North Carolina. It reported 5 killed and 27 wounded of the 453 engaged at Iuka , had 19 killed and 62 wounded at Corinth, and sustained 81 casualties at Hatchie's Bridge. Many were disabled in Tennessee, and early in 1865 its ten companies were reduced to three and the unit was redesignated the 37th Battalion. It surrendered in April. The field officers were Colonels Orlando S. Holland and Robert McLain; Lieutenant Colonels William S. Patton, Samuel H. Terral, and William W. Wier; and Major John McGee. [NPS Soldiers & Sailors System]

******************
Here's another with a similar name.

Robert G. C. Hamill, 22 year old Farmer, born in Louisiana, enlisted as a Private in Company H, Taylor Regiment Texas Mounted Rifles* March 20, 1862 at Fort Washita, Chickasaw Nation, enlisted December 13, 1862 in Taylor's Regiment Texas Mounted Voluteers at Whitesborough, Texas, promoted to 2nd Sergeant May 1, 1863, his name appears on the February 29,1864 muster roll at Harrisonburg, Louisiana, no further records, this was the latest muster roll extant for this company

** The 22nd Regiment Texas Cavalry was organized January 16, 1862, and re-organized June 30, 1862, with ten companies, A to K. It appears to have been reduced to a battalion of six companies, A to F, some time after February 29, 1864. The organization was known at various times as the 1st Indian Regiment Texas Cavalry, Merrick's Regiment Texas Dismounted Cavalry, Taylor's Rifles, Stevens' Regiment Texas Cavalry, Taylor's Regiment Texas Mounted Rifles, Stevens' Regiment Texas Cavalry, Stone's Battalion Texas Cavalry and Merrick's Battalion Texas Infantry or Dismounted Cavalry

M323: Compiled Service Records of Confederate Soldiers Who Served in Organizations From The State of Texas