Jeff, the reference to "teamster" means that he was detailed to drive a wagon and team on April 22, 1862. Each regiment was authorized a certain number of wagons to transport camp equippage, rations, and other regimental property.
In his pension application, did he state that he transferred to Brooks' Regiment or to the 26th Arkansas Regiment, or both?
Brooks' Regiment was the 34th Arkansas Infantry, and Frank Elliott is carried on the rolls in Company G. The records indicate that he enlisted in Sebastian County on June 26, 1862. The last surviving muster roll of this company, for the period ended February 29, 1864, states that he was absent on furlough.
The 26th Arkansas was an entirely different regiment, and there's no record of him in that outfit.