is that your S7 Lionel ? a beautiful example if it is, as you say some of the Sunbeam purist's consider it to be a BSA
That is a wonderful picture of Laytons, makes you wonder where all those bikes are now ? I have attached a photo I took at the Ace Café London of a Brough Superior, I think it is an old SS100 like my dads, Laurence of Arabia famously died crashing one as most people know who like these amazing machines.
My dad also had an Aerial Square 4 which had the problem of the 2 rear cylinders overheating, I wonder did the Sunbeams have that problem with the rear cylinder ?