First off, I would toss out the England death data. I have a whole group in my family from that same "Global, FindaGrave Index" that are mistakenly placed in England when I KNOW they were in Texas. It's some glitch that's giving bad results.
Is Edgar Caswell Ellinton kin to you? He seems to be living in the same area as another Ellington family that who I think is your gr-gr-grandfather's. In the 1850 Census Calvin Ellington, born circa 1830, lives in Randolph County, Georgia. Interestingly he seems to have been counted twice - once in the household of James Ellington (his father if the FindaGrave listing you shared in your other thread is correct) and the second time in the household of M. Ellington where his occupation is listed as "overseer." That these two men live nearby gives a lot of confusing records returns but it looks like they could be sorted with some patience.
As to Civil War records, I can't find anything linked to a soldier with the first initial E or a Calvin or anyone in Georgia named Ellington who seems to fit your guy. I found an amnesty application from Edgar C. Ellington from Quitman County, Georgia which claims he had been a staunch Union man earlier in life and "took no active part in the war, not having for a single hour born arms in any capacity against the government of the United States." If this is Edgar Caswell Ellington he must have thought of any "home guard" duties he had after being put on the muster roll in Quitman County in 1862 as being purely defensive and not an act of war! Or he did so little that it didn't seem to count. Maybe he went out unarmed, which I suppose was possible, though foolish.
As to the Calvin Ellington living in Randolph County in 1850, I can find no further record. That he doesn't have a CSA record doesn't mean he didn't fight. The name could be terrible mangled in the records. He could have served in a home guard unit that didn't get formally enrolled into the Confederate Army. He could have gone off to enlist and gotten sick or killed before getting into a record.