First off, try a Goggle search, 8th Missouri Infantry. The first hit lists a complete roster of the regiment.
I find two William Andrews in the Company roster.
William L. Andrews
Residence was not listed;
Enlisted as a Sergeant (date unknown).
"E" Co. MO 8th Infantry
&
William Andrews
Residence was not listed;
Enlisted as a Private (date unknown).
"E" Co. MO 8th Infantry
The US Army Military History Institute, Carlisle Barracks list the following documents in their unit bibliography. Captain Pirnell's certainly looks of interest.
George Martin
USAMHI
HistServices
9 Nov 03
8th Missouri Infantry Regiment (Mitchell's)
Confederate Military History, Extended Edition. Vol. 12: Missouri. Wilmington, NC: Broadfoot, 1988. E484C65.1987v12.
Contains numerous, scattered references to Missouri units.
Crute, Joseph H., Jr. Units of the Confederate States Army. Midlothian, VA: Derwent Books, 1987. Ref. See p. 202 (1 photocopied page) for a concise summary of the unit's service.
Pirnell, Eathan A. Serving With Honor: The Diary of Captain...of the Eighth Missouri Infantry (Confederate). [Ed by Michael E. Banasik] Iowa City, IA: Camp Pope, 1999. 431 p. E569.4.8th.P56.
Sifakis, Stewart. Compendium of the Confederate Armies...Missouri.... NY: Facts on File, 1995. p. 124 (1 photocopied page). E547S53.