I'm somewhat familiar with Thomas Jackson Thurman, but I haven't been able to prove that he connects with the Thoroughmans. I had believed for a while that he was a brother of a George W. Thoroughman and another William Perry Thoroughman (not yours), but this theory may not be true, as custody papers for George W. and William Perry show them to be children of Samuel Thoroughman (c.1795-c.1832) and no such papers seem to exist for Thomas Jackson; this doesn't disprove my theory, but it doesn't help it either.
In my opinion, Thomas Jackson is probably related somehow to the Thoroughmans -- especially since he had a son named William Perry, who seems to have been named after the other one. But I'm not sure how he fits in.
Could you let me know more about the lineage from Thomas Jackson to yourself? I have some information about descendants from two of his children by his first wife, but none through William Perry.