I have a bit of information about John in my files. He was married to Eliza Rodgers as this note shows:
Eliza Rodgers, b. ca. 1842 Married 7/01/1868, Jefferson Co., IN Spouse: John H. Finehout
Eliza was the daughter of James Rodgers, brother to one of my direct ancestors, Charles M. Rodgers.
My notes for James include:
1850Census, Jefferson, IN, p137, another James on p105; Hoosier Journal of Ancestry, Jefferson Co marriages, 1834-1841.
CENSUS:1850 Jefferson, IN p138 (household?) right after Charles and Ephraim James Rodgers 53 PA Eliza 49 PA Ephraim 11 IN Rachel 10 IN Eliza 8 IN James 17 IN Rachel 78 PA
James Rodgers m. Eliza Rodgers on 5/02/1837, Jefferson Co., IN. He would have married her when he was about 40 yrs. old. She was most likely his second wife. Eliza was born ca. 1801, PA.
I don't have direct records of the following, but some researchers claim Charles, Ephraim, James and a couple of other Rodgers men are sons of Robert Rodgers. All are evidently from Pennsylvania, arriving at Madison, Indiana, soon after 1812.
Please let me know if this helps. I would love to compare notes with you and give you what help I can provide.