These people lived in liberty Twp in Washington County Ohio. The Census indicates that Joseph was born in PA and Rebecca in Ohio.
I have other information from this line for the George Thomas Gearheart who was the son of Joseph. He is my gg grandfather. I am copying and posting what I found at the genealogy library in Marietta Ohio.
Family Tree of Joseph Gayhart ( Known to us as Joseph Gearhart)
Jospeh Gayhart b. 1810 d. 1890 m 1. unknown child. Jane Ann
m 2. Rebecca
7 children George 1845 Rachel Anne 5/12/1844 Joseph Mary Robert Lindsay Martin Matilda b 1858
(My Note: Here is where the Census proves that by 1860 Joseph was living alone with his children and possibly a hired girl if memory does not fail me.My guess is Rebecca died in 1858 at the birth of Matilda. She would have been 34 years old.The person who submitted this has wife number 3 listed as coming after Rebecca and being a Byersock. I would think maybe Rebecca was the Byersock because grandma said her great grandmothers name was "Bryermaster" and that is close.
Joseph Married Matilda Farley in 1862. She was a widow. Here there are two children listed to Joseph and wife number 3. That was Maggei and Josephine. Maggie Married John Chernault. My thought is these may be step kids.Matilda had kids by her first husband because I have been in touch with a researcher who descends from them. Joseph then married for his 4th wife Eliza Moore in 1868 and while they do have a 4th wife listed her name is not. )
They have GT down here as only having two kids--Johnny and Joseph but we know there were others. Rachel Ann Married Jake Burford and had nine kids. Ellie m weaver2 child Bryan and Ralph Florence m Martin 3 child Gyndlou, Geneveve,Wayne Dan 1 child Cecil Hiram 6 child Straucie, Flossie, Ethel, Glovena,Della, and Jessie Joe m. Bessie Wilson 3 children all died in infancy Reuban 1 son Emil George 5 child Leonard, Beatrice, Doanald, Leslie, Louise. Efranum 7 child Eva, Carl, Bill, Mary jo, Rebecca, Clara, Louise. Girl ?? 1 child Susie
Matilda m Eph Thompson 5 children Elizabeth Mary Etta Belle Edward Theodore ( Tench ) m Cora Hufford 7 child Jaunita, Helen, Dennis,Dorcus, Fred, Clarence, Nellie Mae. 2 unknown infants
Joseph3 child. Joseph Johnny unknown girl
Robert Lindsay m Jane Dunlap 5 children Arthur died at 7 years Ida Mae m John Berkheimer 2 children James Grant m Gertie Van Arsdel 4 child Cecil, Eileen, Mansel, Nadine. Joseph died in infancy Annie Belle m Ira Edwards no children
Martin M. Annie Bush 1 child Anna Bell
By Joseph's 3rd marriage
Maggie Married John Chernault 4 child Emmet m Ona Wright 1 child Arlene Walter m Palona Palmer 2 child Opal and Melvin Nellie m Barney Wells no children
Josephine M Sam Atkinson 7 children Harve Nellie Maggie (Darlene Bass Grandmother) Ray disappeared Lenny m Gazzella Valentine Groce Sadie Genevive Written by Letha Tritle and Della Fox