There is a student named Hannah Gibson in the student rolls of the Mordecai school, which I assembled for my 1996 dissertation. She was at the school from mid-1812 to the end of 1813, so three sessions. I don't have a hometown, a parent name, or any other details in that appendix. So I'm not sure what we'll be able to find now, almost 30 years later, but let's have a look around anyway....
Well, here's one candidate who fits the part: a Hannah Gibson from North Carolina, born in 1800, daughter of Thomas Gibson (b. 1763). She first married in 1819, to George Crothers (or Cruthers) in Randolph County NC. She married again in 1831, to a divorced man named Pierce M. Nixon Jr., also in Randolph County. They were still living together in Randolph County for the 1850 federal census, along with a neighbor's child, George N. Allred.
So, she's the right age and place for a Mordecai student; still, no "gotcha, aha!" connections so far. And her first and last name aren't distinctive enough, in isolation, to say this is the one. But it's the best possibility I saw.
