A William L. McCarver served briefly as a private in the 1st Arkansas Mounted Rifles in Company H. A man named Dacus published a history of the 1st Arkansas Mounted Rifles, which was mainly a history of Company H. He includes a lot of personal information regarding the men of Company H.
If this man turns out to be the man your are researching, you may find some good information in Dacus' Book.

William L. McCarver orginally enlisted at Pine Bluff Arkansas on July 25th 1861, in Company B in the 9th Arkansas Infantry. B Company nicknamed the "Cutoff Guards" was organized in Drew, County, Arkansas. he was absent on December 31st 1861 as he was on detached duty as a teamster.

He was transferred to Company F, 9th Arkansas on April 17 1862. He was absent on Furlough (sick leave)on August 31, 1864. He was transferred to Company H of the 1st Arkansas Consolidated Mounted Rifles on April 9th 1865, was present for duty on April 30th 1865, was paroled at Jamestown, North Carolina on May 1, 1865.

As for Tennessee Service, I found reference to William McCarvers in 4 diferent Tennessee Infantry units.