I've heard people today wonder why they are all wearing "bow ties" in period photos, but these were the ties of the era; I don't think the modern style necktie came into fashion until the late 19th century. The cravat was not something a soldier would typically wear while in the field, but my understanding is that it was considered socially correct when in mixed company back home, sort of like a vest, and was a typical piece of civilian attire. Not always worn by working class men out in the field though.
A few examples:
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Lt. Col. Benjamin Franklin Carter of the 4th Texas Infantry.
Unidentied Texas Confederate, ca. 1861.
Missouri State Guard soldiers: Private S. W. Stone (left) of the California Guards and Private P. S. Alexander (right) of the Moniteau County Rangers.
Jesse James
Private Joshua W. Whaley, Co. G, 34th Alabama Infantry.
Portrait of an unidentified University of Virginia student who joined the Southern Guard, a Confederate company formed in Charlottesville which became part of the 19th Virginia Volunteer Infantry Regiment, c. 1861.
Sergeant John Emery
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Joseph Sharp, 1849 gold miner of Sharp’s Flats.