Found your inquiry.Welcome to the Makemson Genforum.
I am sure you have quite a bit of information already in finding your grandmother.
I do have information that I would gladly share.
Elizabeth Makemson - I have a birth date of 1792 in Harrison County, KY.Your date of 1762 would mean that the Makemsons were in Ky. by that time.However, it appears to me that they were still in Maryland as the Battle at Ft. Mifflin, involving many Makemsons, was not until 1777.
I show John Makemson, born before 1750 either Scotland or Ireland.Death 1814, Harrison County, KY.
I have Elizabeth Brown, born 10-15-1754, Fawn Twsp, York County, PA.Death 1833?, Harrison County, KY.
The name.Research shows the great possibility that the name may have been some spelling of Malcomson.We do have dates back into the 1600's in Northern Ireland, County Armaugh.
I have cousins with the spellings of Makamson and Mekemson who correspond.