Mine's very roughly around 18"/450mm/2 span.
Cannot be more accurate as no tape measure ........
Are you going to have a fixed fairing or one you can move/swing forward to help you get on and off ??
If fixed then the best method for the back support is to extend the line of the derailleur post.
My post is ~15" to just under where the back bow is and then I've a short bracket (~4" tall) to fit the fairing at the correct height.
This gives you the maximum room to swing your feet out sideways before standing up.
Your other option is just a vertical post off the main frame.
It will be harder to get out past it but thats where it tends to be for a moveable fairing.
It's slightly more tricky if you make it so it swing/lifts forward as you'll need some type of hinged/quick release joint.
Not to sure how to design that as my fairings have always been fixed.