Here is what I could find on William Gallatin Paxton. First let me say that part of what is said on the findagrave memorial site is probably in error as pertains to Morgan's Cavalry. Records do indicate that a Wm. G. Paxton was promoted from Lt. of Adams' Cavalry to Major of Miller's (9th Mississipi) Cavalry.

http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Paxton&GSfn=William&GSmn=Gallatin&GSbyrel=all&GSdyrel=all&GSob=n&GRid=13995386&df=all&

http://www.mississippiscv.org/MS_Units/9th_MS_CAV.htm