I've read that it works with the Graflok back, but mine is cheaper (?) and has the leaf springs on the back. I've used the Fuji PA-45 back before simply by loosening up the screws holding down the leaf springs. Is the 405 thicker than the the PA-45 though?
You have a Graphic Back. It was the original design used on the introductory speed the Top Handle Speed Graphic in 1912 through the first 2 to 3 years of the Pacemaker Graphics until the Graflok became the standard in 1951 or 1952. In other makes of cameras they are referred to as the Spring Back and the International back.
Doing some research on Graflex.org the Polaroid 405 was made for Graflok/International backs. If you have a Crown with a Kalart or Hugo Meyer side rangefinder calibrated to the lens you plan to use or a top mounted Graphic rangefinder with a matching cam for the lens in use then you can remove the focus panel of your Spring back or Graflok back, attach the 405, rangefinder focus, and use either the Sports finder or the Optical View finder if so equipped.
See
http://www.cameraeccentric.com/html/info/graflex_5.html if you have trouble with some of the camera terms.
Edit: the screw that holds the focus panel leaf spring to the back is a #4-40, a common hardware store size. The original is 5/16 inch long. A flat washer can be cut so that it has a flat edge and sits on the lip of the 405 to hold it in place.
From pictures the 405 is 3 to 4 times as thick as a standard 2 sided film holder.