In The Dickson Letters, James Dickson, youngest son of the 1704 John Dickson of Duplin Co, NC had a son named William Dickson who was supposedly born in NC in 1781. The Dickson Letters gives the names of James Dickson's children and I have a copy of his will where William is named as an heir. Your William Dickson lived next to my John M. Dickson in Maury Co TN where John M. died in 1819. Elizabeth Dickson, wife of John M. came to Hardin Co with her family about 1824. She and your William lived near each other. My John M. Dickson was the son of John Dickson c1737, an older son of the 1704 John Dickson and older brother of James Dickson.
You can get to The Dickson Letters on line at the http address that Donna gives in several messages down from yours. I think it was message #3126.