Wesley W. Faulkner (age 23) is listed as a Teamster with Co. C, 5th Reg Infantry Volunteers, Capt Bradford, Enlisting at Cove Creek Arkansas, Feb 23, 1862, "left with team from DesArc Arkansas", native of Boliver MO.
Assigned to Trans-Mississippi Dept.
Sounds to me as if he may have been one of those that "deserted to fight at home" or maybe he was hauling supplies for Clark's Regiment and was picked up in the afore mention McNeil action.
Coincidentally, the 1860 census does not help us much.
There is a Wesley Faulkner 22, son of James and Rebecca Faulkner Looney, Polk Co, Missouri dwelling 812.
There is also a Wesley Faulkner son of William and Elizabeth Faulkner, 22, Kennett, Independence, Dunklin Co, Missouri, dwelling 808.
If we accept the service card entry that he was native of Boliver MO then the Polk county fella is likely our man. So now comes the twist, which Wesley Faulkner was actually captured Dunklin Co March 1863? They both have reason to be there. If he was a teamster, the Union authorities may very well expected him to be a civillian under contract leading to the label confusion when he got to prison.