[rotorwrench]

Most of the old Ford fordor sedans have structure back behind the seat to hold the seat back and even the spare tire sometimes. The rear shelf is generally just some cloth covered panel board using a cloth to match the head liner or rear seat material. Some of those panel boards were steam formed to a specific shape to fit the recessed area better then covered with the cloth and possibly even some jute padding. It would likely have some screws to hold it in places that can be covered by the rear seat or at least some shiny screws and trim washers where they can be seen. It would only take a few screws to hold it since the rear seat likely also helps to secure things a bit.

I've never done a 1940 sedan but I've seen a few of them after they were redone.