There is a recently published history of the 12th Illinois Cavalry.
Blackwell, Samuel M. Jr., "in the First Line of Battle - The 12th Illinois Cavalry in the Civilw War", Northern Illinois University Press, Dekalb, IL. 1st ED., 2002, 22 pages.

I have not found Edwin West mentioned specifically in the book.

Il Adj General's Report, Vol. 8, page 353 Lists Edwin West Residence Augusta, Date of rank or enlistment Jan 15, 1862, Date of muster Feb 24, 1862, Remarks Re-enlisted as Veteran.

Members of my extended family were not discharged until 1866.

Christopher Ward, LeRoy Ward, John Irish all from Northern Boone County, IL.

There is some information on the 12th Illinois in:

Wittenberg, Eric J., "The Uniun Cavalry Come of Age - Hartwood Church to Brandy Station, 1863", Potomac Books, Inc, Washington, D.C. 1st. Ed., 2003, 390 pages (softbound)

The 12th IL Cavalry does have Reuniun papers published, one of which is October 5, 6, 1918. This is the Abraham Lincoln Presidential Library in Springfield, IL along with other information on the 12ths campaigns. If you go there, check ahead in their online book catalogue. The librarians there are very helpful.

The used to be a Web site, Called "Bufford's Boy's" that had information on the 12th, but I can't seem to find it.