I was able to find on the 1910 census for Chicago a abt.born in 1862 New York James Dixon, age 48, married for 25 yrs to a Katie Garrigan, age 49, with one son John J, age 17, and Katie's widowed brother Michael,age 50, living with the family.
I don't find any other James E for IL afterwards.

On the 1870 census for Hamilton Co, IL there is a Columbus age 16, William age 10, James age 8 and Henry E Dixon,age 2, all born in IL, living with Joseph Witham, age 23, and Mariah, age 25. Because of the ages, Columbus could be Mariah's brother. Maybe some of these names will help you with your search.
My Dickson - changed to Dixon by Govt during release from Civil War - family is a whole different matter. I know that my GGG grandfather was John William Dickson lived in Iroquois Co., IL from 1867 til 1914 time of death. Married Mary Ann DeWitt in Clifton, Iroquois Co., IL in 1867. John William name was changed from Dickson to Dixon when he was discharged from the Civil war army. Tombstone still reflects Dickson but children and some property were done in Dixon. John and Mary had 2 children Eva and Earl. Earl stayed in the area and was married 3 times. I have little info on his family. I am from Eva. To contact me email me at elh754@prodigy.net