The service records indicate that most of them died in September of 1862, but a few in November as well. The 16th Texas was stationed at Camp Nelson at that time. In the case of Private Levi Brinley, the record states:

Sept. 1862
St. Jno's {John's} Hospital
Died of disease

Other sick men are listed as being in the hospital at Austin, Arkansas, which is a little ways south of Camp Nelson. So while it is not out and out stated that they were at Camp Nelson, from the movements of the regiment it is reasonable to assume that they were among the 1,500 victims of disease there. I will be happy to provide dates and locations from each if you would like to have them.