His birth announcement in Quaker meeting records lists his name as Eli, so I do not believe it was short for anything. He apparently also had a brother named Elisha. According to Quaker meeting records, he was in trouble by the Quakers for having been married by a hireling minister and for "using strong drink to excess." He died between 2 Feb 1865 and 2 Mar 1865.
An 1880 marriage certificate for his son Collins states his name as "Elia Griffith" and his birthplace as "Wales," though other records confirm he was born in Pennsylvania.
Eli was born 1794. Eli Griffith ... [1]
U.S., Encyclopedia of American Quaker Genealogy, Vol I–VI, 1607–1943 Name Eli Griffith Birth Date on Image 16 Fifth 1794 Translated Birth Date 16 May 1794 Birth Place Fayette, Pennsylvania Monthly Meeting Providence Monthly Meeting Volume Encyclopedia of American Quaker Genealogy Vol. IV
An Elia Griffith was disowned by the Quakers in 1865 for "marrying again while his divorced wife was still alive." This is most likely a different Griffith given that his wife, Rachel, died in 1851, but I have yet to figure out who this could be.
U.S., Quaker Meeting Records, 1681-1935, Wayne, Indiana, Certificates of Removal, ancestry: page 87 out of 105
1850 United States Federal Census
Name Eli Griffith
Age 56
Birth Year abt 1794
Birthplace Pennsylvania
Home in 1850 Wayne, Wayne, Indiana, USA
Gender Male
Family Number 96
Household Members
Name Age
Eli Griffith 56
Rachel Griffith 57
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Eli Griffith Residence Date: 25 Jun 1823 Residence Date on Image:25 Sixth 1823 Residence Place:Belmont, Ohio Spouse:Rachel Griffith & son William Event Type:Removal Monthly Meeting:Concord Monthly Meeting Approved & signed https://www.ancestry.com/interactive/2189/31906_266751-00087?pid=1312890&backurl=https://search.ancestry.com/cgi-bin/sse.dll?db%3DQuakerMeetMins%26h%3D1312890%26indiv%3Dtry%26o_vc%3DRecord:OtherRecord%26rhSource%3D2189&treeid=&personid=&hintid=&usePUB=true&usePUBJs=true
A certificate was read and received for Eli Griffith & Rachel his wife from Chesterfield Mo meeting Athens Co Ohio, certificate dated 15 day 11 month 1842.... a visit was planned. https://www.ancestry.com/interactive/2189/40780_293040-00721?pid=446493&backurl=https://search.ancestry.com/cgi-bin/sse.dll?db%3DQuakerMeetMins%26h%3D446493%26indiv%3Dtry%26o_vc%3DRecord:OtherRecord%26rhSource%3D3753&treeid=&personid=&hintid=&usePUB=true&usePUBJs=true