Hi again Kaz
I think Sapper T Patterson in the Stockton Book of Remembrance and Sapper Thomas William Patterson on the CWGC are likely to be the same man.
If you search the CWGC website for
T Patterson in WW2, only 13 results appear, all of them called Thomas or Thomas Something Patterson.
Only 2 of them are in the Royal Engineers. You can rule one out as he was a Corporal (son of Percy and Marjorie Patterson, of Jesmond, Newcastle-on-Tyne)
The only one left is Sapper Thomas William Patterson that you have already found. He has to be the same Sapper T Patterson of the Royal Engineers who is in the Book of Remembrance at Stockton.
I would take Girl Guide's advice and order his service record if funds allow.
Good luck
