Searching for info on Alex Eller

Hello - I am looking for any information on my 4x great grandfather Alex Eller.At this point all I know about him is his name which I got from my 3x great grandfather's (John H Eller)death certificate.
John was born in Carlinville, IL in 1848 and died in Staunton, IL in 1936.His death certificate shows Alex as his father but does not have any other information about him.
I am hoping someone may have evidence that Alex may be a child of Peter Eller, as I have his in my tree connected to other people, so much to the point that I have to believe he was related.Based on John's birthdate I assume Alex would have been born somewhere in the 1820's or very early 1830's.
To give you a little more information that might help narrow him down, here is some of the information I know about John (Alex's son).John first married Nancy Hampton on Oct 16, 1869 in Macoupin County, IL and had my gg grandfather Charles in 1873.I believe Nancy died as he married Rosa Ann Eller (the daughter of Powell Eller, a confirmed son of Peter) on Oct 20, 1874 and had three more children: Preston, Rosa Elizabeth, and Bertha.
If anyone knows anything at all about Alex, I would really appreciate the help!

Thanks so much!
Angi