Also in these CSRs under the Unit Identification section is this listing of officers:
Company F Officers
John Muller, Captain, Company F, resigned October 4, 1862
Jackson S. McMahan, 1st Lieutenant. Company F, Captain Company F to Captain Company G, died December 4, 1862
Company G Officers
John W. Hood, Captain, Company G, resigned August 8, 1862
Jackson S. McMahan, from Company F to Company F, there is a Number 2 alongside the notation Captain, which I would assume to mean he was the 2nd Captain of the Company, there is a C. C. McGinnis, 1st Lieutenant, then Captain with the number 3 alongside, perhaps meaning the 3rd Captain
From this, I believe McMahan assumed command of Company G in August, and returned to Company F on the resignation of John Muller, October 4, 1862.
Suggest you find a library which holds the Supplement to the Official Records, Broadfoot Publishing Co., Wilmington, N. C., and study the Record of Events for the 2nd Texas Infantry. You can contact Broadfoot to find who holds these volumes in nearby libraries. Or, you could check with World Cat through your local library.
The citation of the companies travels was taken from The Companies Record of Events found in the Compiled Service Records of the regiment and in the Supplement to the OR as previously noted.