If you are still interested in researching your Patrick County ancestor who deserted, you may want to read the following https://vtechworks.lib.vt.edu/handle/10919/36663. It is a disertation about deserters in neighboring Floyd Co., VA. While it may not answer specific questions it may shed light on what was going on in the area at the time period your ancestor deserted. My ancestor, Randolph Cannaday, also enlisted in the 51st VA Infantry and deserted 5/18/62. He was arrested by the Floyd County Enrolling Officer and jailed in Floyd Co for 11 days. Unfortunately, I have not been able to find anything after this date that show if he was returned to the army or what happened to him. But as I stated the about work does shed light on the happenings during the difficult strife in the area.