It is important to note that Col. Nathan GALLUP's mother was named Eunice. Names do repeat in families.
This is problematic because Col Nathan GALLUP (Sr.) was married to Sarah GIDDINGS and she died in 1778. There is no vital record that I can find that indicates that Col. Nathan had another wife named Mary. I returned to the oldest Gallup genealogy because it is out of copyright and at Google Books. It is searchable. Mary doesn't appear as another wife.
Since Ancestry.com released the US Wills & Probate records, I searched for Col. Nathan GALLUP and found his will. In it was a page listing his bequests to family members. I was so pleased to find that it listed another wife. Her name was Mary.