I also have an Andrew Thompson from Davidson Nc
in my tree.
Andrew Thompson married Tamar Cameron.
Tamar is est b. in 1788 per headstone
d.10mar1812 age 20
Andrew ismentionedon her stone as husband
This Andrew is son of
Wm Thomson
who moved to Rowan 1774 from NJ
This Andrew was b. 20oct1787
There is atleast one son mother unk
Thomas B. Thomson

WhereThis Andrew went i dont know.
Perhaps hes your Andrews kin.
Thom C.