Unless he had a previous marriage, this wouldn't work for Elzy since he was born in 1872.
However, there does appear to be a previous marriage:
Arkansas Marriages, 1779-1992 about Milus Vansickle Name: Milus Vansickle Marriage Date: 22 Mar 1866 Spouse: Elizabeth Rowe County: Hot Springs State: Arkansas
Here is the family in the 1870 Census:
1870 United States Federal Census about Miles Vansicle Name: Miles Vansicle Birth Year: abt 1846 Age in 1870: 24 Birthplace: Arkansas Home in 1870: Hot Springs, Hot Springs, Arkansas Race: White Gender: Male Value of real estate: View image Household Members: Name Age Miles Vansicle 24b. 1846 Arkansas; farmer Elizabeth Vansicle 22 b. 1848 Prussia Ora B Vansicle 3b. 1867 Arkansas Sarah Vansicle 2b. 1868 Ark. Thomas Vansicle 1b. 1869 Ark.
This Thomas appears to fit as a possible brother to your Elzy.Unfortunately, I can't find the family in the 1880 Census.
There is a tree on Ancestry.com that has Elzy b. 1872 as son of Miles William Vanstsickle & Elizabeth Rowe along with son, Thomas M. b. 1869.The line traces back with the names you suggested.It's a well sourced tree with photos and family bios.Good luck in your search!Annie