Why a soldier deserted has more to do with the commanders. Good commanders did not have deserters. I am talking of company commanders. This is where a soldier is affected. Even good Generals had desertions. One of the companies I am studying, had almost half the company desert in a three day period in late August 1863. Some came back, but most did not. Many soldiers were sick of the war, and some were scared after seeing so many friends die. Some were hungry, stopped and never caught up. Many reasons.
You can keep looking. Some towns kept records. We are finding data about a major who died in February 1864. A diary described his death 9 days after the battle where records say he died. These notes have led to his grave, which we hope to mark this year in Jackson Mississippi. This is a hundred and forty eight years late, but I plan to drive from central Texas to help.
Many soldiers felt responsible for their friends families. Some loved the letters that were read by the camp fire. Again, many reasons.