I have a list of cemeteries in Licking Co (current & extinct) & I don't find a Mt Carmel Christian Union Church Cemetery; the closest I found in this county were Mount Calvary (Catholic) & Mount Pleasant Cemeteries. I checked the current phone book & there is no listing for that church (my old directories are packed away so I couldn't check that). I did find an Aaron WALKER 20 Jan 1798-21 Aug 1891 buried in Mt Carmel Church Cemetery, Pleasant Co, WV & I found a Mt Carmel Church Cemetery in Salt Creek Tp in Hocking Co, OH. I, too, have a few WALKERs descended from Gideon WALKER if I remember correctly. Good luck with your search &, if you do locate it in Licking Co, please let me know & I'll add it to my list. Thanks.