People moved frequently, particularly during the mid-19th century. Many men found on the 1860 census in a distant state can be found in Texas Confederate units because they moved shortly after the census. It's also not unusual to find men in Alabama Confederate units who might be identified on the 1860 census hundreds of miles to the north or east.

In practice your method usually works, and you are to be congratulated for the research presented on family location. This is most helpful to other researchers when posting inquiries.

The Texas soldier mentioned is a reasonable candidate, but enlisted in Houston TX at the age of nineteen. He can be ruled out for that reason. A man named William M Givens, age 31, enlisted in Co "E", 2nd Alabama Artillery Battalion, Mobile AL, Oct 25, 1861. Age, first and last name matching, and there being no other men named William Given or Givens living in Mobile in 1860, this must be your ancestor.

Further confirmation - on the 1860 and 1870 census of Mobile AL, the occupation for William Givens is given as carpenter. During his Confederate service William Givens was assigned to work as a carpenter.