After reading all the response to your post, I had to write to let you know that our relic group, CARHA, cares for the Silverdale Confederate Cemetery that you have found out about. It is the burial ground for 155 soldiers from Withers' division hospital that was at Tyner's station. Until we started a number of years ago all were unknown. We have placed 6 tombstones for people like yourself who find their relative died here.
Your relative probably died as a result of poor sanitary conditions from his stay in camps near Corinth and Saltillo. Shallow wells and mosquitos were the cause of diseases like dysentery, chronic diararhia, malaria, etc. The doctors had many names for things that are not used any longer such as dropsey, flux, etc. So many men were sick at this hospital that, when the army marched away on September 30, 1862. the hospital stayed behind. Your date of death for Lindsay Partridge, November 17, 1862, is consistent with the hospital being at Tyner's station. The hospital was sometimes listed as Cleveland and moved there about the 15th of December into brick buildings as the tents became too cold for the patients.
We would be happy to assist you in obtaining and placing a marker for him. The Veterans Administration provides them and we set them in our cemetery. We get the flat granite ones since we have to mow over them. Complete birth date and death date or birth year and death year are the only choices the VA allows so please find his birthdate if you can.