Just judging from the records of Co "K" 33rd Arkansas and the number of men from that company that died at Camp Shaver/Camp White Sulphur Springs, I would say that there was a lot of sickness in the 33rd Ar. while at Sulphur Springs.
Secondly given the poor records keeping of the early regimental and company sargeants especially during July and August 1862 at Sulphur Springs I would say the the odds of Eli being one of those casualities dieing of the Measle, Pneumonia and Camp Fever would be very highly likely. Especially in the absence of any other records otherwise of the man.