Check fold 3 again no luck for 42nd, but did find a W. W. Pearson in the 36th Miss. This man appears to have died in 1862. Did see one W.W. Pearson in 2nd Georgia Cav. Checked this website https://www.nps.gov/civilwar/search-soldiers.htm#sort=score+desc&q=W.+W.+pearson cannot find your man here either.

GP