If the John Sheen,born 1833,Ireland from the 1871 census is a John Sheehan,and Jeremiah Sheehea of the 1881 census is also a Sheehan,I could make this highly speculative relationship and family:
In 1861 and 1871 there is a Mary Sheehan,mother in law to a Johannah Hourigan or Horrigan at
RG09 4012 19 39
RG10 5338 26 48
It is part of the speculation that this is the same family as John and Jeremiah,but does not need to be the case for their relationship,I was simply looking for early evidence of the Sheehan family "in the area"
The following records are from
www.irishgenealogy.ie(free site) and all are Cork South
At least the following are children of Edmund Sheehan and Mary Murphy
Denis 1826
Mary 1828
Johannah 1829
John 1832
and then
Jeremiah 1852 to Denis Sheehan and Johannah Madden(the witness/sponsor is an Ellen Mahony,but this could be just another coincidence)
(Jeremiah calls his first born Johannah after his mother?)
This would obviously make John the uncle of Jeremiah
As I said all very speculative,there are so many variants of the name.Perhaps another link could be found to enhance the credibility.I'm not sure it goes to the core of your search but might be an interesting avenue(hopefully not cul de sac)
Regards
Roger