I don't have a SENA POOL in my tree, and in fact my ancestors seem to have migrated from NC to GA and then to AL, and skipped SC completely. However I do have some possibilities for you to consider; from the 1800 census in SC. She would be 13 if the 1787 birth is accurate:
Those were only 4 female Pool's I found in the entire state in the 1800 census with a female that matched the age range of your g-g-g-g-grandmother. A lot of parents named their kids after their parents, siblings, grandparents, aunts & uncles, etc, so review other year census information for these people and see if you recognize a lot of names, that could be a clue.