I've done a bit of research on William. I added his 1850 and 1860 census records to his profile. Those I am certain of. He is in Mecklenburg w/ a son W. W. and his daughter Elizabeth just before she married.
As for his origins, I didn't see much. I was able to find what I believe to be his 1820-1840 census records using info from his profile and the bible transcription on his FAG memorial. Not enough detail in those.
In the 1820 census, I believe that is William on page 3. The only other Allison I see is a William on page 2. He is living alone and would need to be older to be William's father.
There was s record of an estate file (below) of a William Allison of Mecklenburg who died in 1815 (no DOB), wife's name Peggy Allison. The proceedings took place in Charlotte. Which is where I found William living. Maybe you can find something in there.
1820, Mecklenburg census: https://familysearch.org/ark:/61903/1:1:XHGH-C5H
Estate file: (https://familysearch.org/ark:/61903/1:1:KDGJ-4H7