A few comments about fasteners and sheet metal. Triumph loved cage nuts, also known as captive nuts. The loose square nut in the metal cage had some wiggle room and the often pointed bolts made assembly quick and easy when the car was new. The TR3 has lots of them, probably over 100 as they are used to attach all of the outer wings as well as the doors, gearbox tunnel, wiper motor, seat rails and even a couple welded to the chassis for the long front tub mounts.
When disassembling a 50+ year old TR3 it will be typical for some to be missing/broken, a small few will undo easily but most of them will be rusted solid and no amount of heat or penetrating fluid is going to free them.
If you are lucky you can get a self grip wrench to clamp the cage around the nut to stop the nut from turning and then undo the nut but in many cases the measure of last resort is to grind off the heads of the bolts so that the panel can be removed and then pry open the cages with a screwdriver to remove the rusted nuts and the hacked off bolts. With better access to the nuts some of them will yield to heat and PB blaster so you can salvage the nuts.
Replacement cage nuts are available and I found the cages acceptable but the nuts were too small and tended to spin in the cages so where I could I salvaged and re-used the old nuts.
Mark Macy in the US sells some very robust cage nuts and I did use them in a few places like the large cage nuts under the chassis for the front floor bolts.
Speaking of floor bolts, many of those are likely rusted solid too and the countersunk bolts at the rear are especially difficult to remove. Stuart's tip was to weld a nut to any troublesome bolt. Welding the nut to the bolt/screw serves two purposes, it gives you something to grip and the action of welding puts a lot of heat into the bolt which helps to break the bond between the bolt and whatever it is screwed into.
I removed most of the floor bolts with this technique.
Finally a comment about sheet metal. The TR3 body is mostly 18 gauge sheet steel There were many times where I needed to make a repair panel but my local hardware store and even my local steel supplier did not stock it. In the end I mail-ordered a couple of 4ft x 4ft sheets from an online supplier. I found the 18ga easy to work with, cutting it either with shears or a cut off wheel.