This family likely originated in England.
The only two known genetic matches are from the defunct Sorenson Molecular Genealogy Foundation public website. SMGF2 traces his lineage from UT, US to Leicestershire to Shropshire. His earliest ancestor is Johannes Gough b. 1557 Marsh, Shropshire, England. SMGF3 traces his lineage from Yorkshire to Leicester. His earliest ancestor is Thomas Gough, b. 1774 Coleorton, Leicester, England. The most likely point of connection between these two families would seem to be Leicestershire in the early- to mid-1700s.
The Athey Haplogroup Predictor was used to estimate the haplogroup as J2a with 100% probability. Since the Athey Haplogroup Predictor was last updated 2012, that year’s ISOGG YSNP tree was used to locate haplogroup J2a and convert to modern nomenclature, J-M410. If correct, this points to an unexpected origin. While the Gough surname is of English origins, YFull https://www.yfull.com/tree/J-M410/ reports that DNA kits in this sub-haplogroup are found around the Mediterranean, Middle East, Near East, Russia and China.
Because the two test kits are orphaned in the defuncted and offline SMGF database, the goal is to identify descendants who can take an FTDNA YDNA37, YDNA67 or YDNA111 test.