The rear sub structure can go either way as far as the rear trunk panel or the curved panel of the rumble seat installation. The sub-frame rear cross member is the major structure back there and then there is a reinforcement for spare tire bracket mounting structure that ties the cross member to the rear body panel.
The rest of it is the two side panels and vertical rear body braces. The trunk panel structure was set up to deal with rain water that will inter on the back side of the deck lid. The curved inner panel for the rumble type deck lid also deals with rain water as a scupper.
If the car was ever converted from a trunk to a rumble seat car then there might be old pieces of trunk panel back there. I've seen all sorts of home brewer panels to replace rusted out rear panels and curved panels so nothing surprises me anymore.
This link is an inner panel for a trunk from Bratton's.
https://www.brattons.com/CURVED-INNER-PANEL-FOR-CARS-W_-TRUNKS/productinfo/35150/
This is a rumble inner panel.
https://www.brattons.com/28-29-COUPE-29-31-CABRIOLET-CURVED-INNER-PANEL/productinfo/35160/
This is the center spare tire brace but it would have to be shortened to work on a 28/29 coupe.
https://www.brattons.com/30-31-OUTER-PANEL-SPARE-TIRE-BRACE/productinfo/35250/
It looks like the spare tire brace is gone. The remnants are small so it's hard to tell what kind of inner panel it had back there.