Anything you find will be "slim pickings" as folks say. You will have to follow the 36th as a whole. Of course, someone
else may tell you differently.
The 36th fought at Helena, where several were taken prisoner including Solomon Moore out of White County
who was a ggg uncle of mine who never came back.
My ancestor and gg grandfather, Sgt. Pleasant H. Loyd, was with the 36th. He survived but died sometimes within
the time after he walked home to what is now White County.
The 36th after Helena marched back through Brownsville and down Military Road. They were somewhere around Little Rock in
September of 1863, when it fell.
There was a history of the 36th written by a Major Price,U.S. military, whose ancestor was with the 36th, but not a Price.
His source was the National Archives. That can be found at the Butler Center.
I believe they surrendered with Kirby Smith in Texas when the war ended.
If you can find the discussion which is in the archives somewhere, you can pick up more information.
Good luck.