Something doesn't jive. About your grandfather you initially said this:
"One of my Great Grandfathers was fresh off the boat from Europe, spoke little or no English, in 1862 volunteered for an Illinois regiment out of Quincy. They served until August 1865."
That doesn't comport with what you said up above.
Is he "fresh off the boat" or isn't he?
We think that by the time their elder son enlisted, in October 1862, his family had been here several years -- I'm calling that "fresh off the boat", as opposed to other ancestors who arrived in New York around 1700.
There were two sons and the story is their family escaped the "old country" in order to dodge its draft into one of Europe's endless wars.
The elder son, my great grandfather, enlisted in the Illinois voluntary infantry.
The younger son, some people claim, though we have found no records of it, joined the Confederate cavalry, ended up in Texas, near San Antonio...
And yes, there is a plausible explanation as to how & why that happened, but we can't prove it.