Its tricky with two hands and easier with a helper- a mirror, flashlight and a cellphone after some cleaning will tell you the partial on the shock tower drop off. Remove one or both front wheels and you can get in there...
I would look inside the trunk. Should be pretty easy to tell if your rear quarter panels are original to the car or somebody welded on a fastback onto a convertible.
I'd look for other "mach 1" features like the honeycomb grille/rear panel, color matched bumper, color matched racing mirrors, gas cap, variable ratio steering box, staggered rear shocks.
You could also look for "convertible" features. I never had one myself. But I believe the part is called the support plate. On convertible cars, its at the very bottom of the car under the rear tail of the transmission. If a car has this, or you can tell one was installed for a few decades, it may be a clue for you.