Well, that DOES change things, doesn't it? I couldn't see a deck lid rumble seat handle in the photo. Missing or did I simply miss it? Is this an original rumble seat or a restorer's conversion? Lots of telltale signs of both, such as extra holes along the top sides of the decklid usually not being filled in after a rumble seat conversion. The lower stop stands are often improperly installed, too.
But let's assume this car was originally a Sport Coupe and not a Business Coupe. There should be special brackets inside the top for landau iron attachment that a Business Coupe wouldn't have had. I believe there is one on top of the wooden belt rail and one up higher on a flat iron bracket. 'Been a long time since I looked at a Sport Coupe top, but I'm certain those brackets/anchors will not be present in a Business Coupe.
At least we know for SURE that it is not a Cabriolet!
Marshall