Other than the horn appearing to be mounted upside down in my photo, that looks like a very good match. And it also explains the uncomfortable seating position of the rear passenger. Thanks! I think you may have nailed it.
I had assumed there was something like a small rumble seat back there.
I probably should have added that this photo was taken in east USA, even though it has a right hand driver arrangement.
The closest thing I've been able to find is the 1911 Cole 30 Model L Roadster, but there are enough differences to examples of that car that I don't think that's it.