Summary: In Ohio Elijah lived right next to a David Cornwell of about the same age, who came from Pittsgrove Township, NJ. David's father is known to have been Daniel Cornwell, died about 1830 in Ohio, very likely the Daniel Cornwell recorded 1793 in Pittsgrove, NJ. It is a good bet that Daniel was also Elijah's father.
From an 1835 deed (see https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSLX-P99Q-6?i=397, right-hand side) we know that the Elijah Cornwell of Clermont County, OH, who was married to Phebe owned land adjacent to the land of a David Cornwell. This land was also adjacent to land of Oliver Crane, John Crane, and Stephen Beck and part of the survey of John Breckenridge.
Elijah's land thus appears to be part of the 200 acres that a Daniel Cornwell of Clermont County, OH, bought in 1808 - that land was adjacent to John Breckenridge's land and to land of Seares Crane (see https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSQ3-1SVT-3?i=214, top of left-hand side, for the purchase), and in 1811 Daniel and his wife (also Phebe) sold 50 acres of that tract to Stephen Beck (see https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSQ3-1SVC-1?i=592, right-hand side).
In 1829 Daniel wrote a will in which he named his wife Phebe and his sons David, John, George, and William (the last three his youngest sons). This will was not probated until 1847 (see https://www.familysearch.org/ark:/61903/3:1:3QS7-L9MK-PD5W?i=105, right-hand side continuing to following page).
In the 1820 census, Daniel Cornwall was listed as over 45 (thus born before 1775) (link for those with access to ancestry.com), while David was listed as 26-45 (link for those with access to ancestry.com).
In the 1830 census, a Phebe Cornwall born in the 1780s (thus probably Daniel's wife or widow) was named right before David Cornwell (also born in 1780s) in Tate Township (link for those with access to ancestry.com).
This Phebe in 1833 remarried to a Jonathan Church and then (as Phebe Church, born about 1785 in New Jersey) appeared in the 1850 census living with Daniel's and her son William and in the 1860 census with Daniel's and her son George (see ancestry profile for documentation).
Given that Daniel's son David was born in the 1780s (per the 1840 census), Daniel was probably born in the 1760s or earlier. Phebe must have been a second wife.
Given all of this, I think it is quite conceivable that Elijah, like David, was a son of Daniel Cornwell's first marriage, and that the reason he was not mentioned in Daniel's will was that he had already received his plot of land before the will was written in 1829 (perhaps at his marriage in 1828).