Looking again, I wonder if the clutter on the left side of the tank is a gear change lever (together with the magneto advance/retard lever and the tank-top toolbox). All the three-speeders (Model H etc.) had the change on the right side of the tank, and to get the change on left we have to go back to 1914 when there were a couple of models with this layout - the 2B with a three-speed hub or the 8 with a two-speed counter-shaft gear. Also there is a hint of "wire", rather than flat, mudguard stays at the front. We could be just pre-war rather than just post-war - a better photo would tell.
Cheers
Leon