Okay, back and ready to deal with the other two Mordecai students named Davis--another Eliza Davis (from Richmond) and Tempy Davis, also from Virginia.
Eliza Davis from Richmond attended the school in its last year, for both sessions of 1818, and has "Major Davis" listed as the adult on her account. ("Major Davis for daughter" is a notation in the school ledger for January 1818.)
Tempy Davis (probably Temperance Davis) of Surry County, Virginia, attended the school only in its last session, the second half of 1818, and has Archibald Davis as the adult name attached to her. ("Baldy Davis for Miss Tempe" is a notation in the school ledger for April 1818. There's also mention of a Baldy Davis attended examinations at the school in June 1826, when it was run by Caroline Mordecai Plunkett.)
Temperance Davis has a more distinctive name, so let's start there.
The Davis-Massenburg Bible in the Warren County Bible Records (I remember visiting those many years ago!) has Temperance Williams Davis (1804-1854), daughter of Archibald and Elizabeth Hilliard Davis, who would have been fourteen when she attended the Mordecai school--a pretty typical age for a student. This Davis family had Surry County roots and branches. And here's the kicker: her younger sister Lucy Henry Davis (1811-1896) is mentioned in the same family source as having attended "the school of Mr. and Mrs. Plunkett" in Warrenton, for four years. This is one of those families where everyone has many children, and uses the same names over and over, but this particular Temperance is a pretty good fit.
Assuming we have the right Temperance Davis: She was one of a dozen children born to her parents; she lost her mother in 1816, when Tempie was just twelve years old. A couple years later, she attended the Mordecai school in its final session. She was sixteen when she married William Williams Thorne (1798-1838) in 1820, and they had at least ten children together in Halifax County, North Carolina. (Their matching middle names may indicate kinship; William's mother was Martha W. Williams.) From the dates of her children's births, Tempe was pregnant for about half of the eighteen years she was married. And then she was widowed, in 1838, at age 34. When Temperance Davis Thorne died in 1854, age 50, her younger children were teenagers, and some of her older daughters were newly married. Here's the William Williams Thorne family Bible to record their marriages and deaths.
And.... I still haven't got around to that other Eliza Davis. I won't forget, but it is a very common name combination.