Obediah mash And William Thacker inquiry

I have read up some on the Thacker theory and heard the same things growing up that one of my ancestors on the Thacker side was full Cherokee. I understand the difficulties with the historical location. I would like some insight as to how to find any information regarding this. If she was of another tribe I’d like to find out. I also have note of a man named Obediah mash/marsh in my ancestry that is said to be Cherokee as well noted as him being a headman and the area he lived in would have been relevant to the time period but I cannot find any other information.