Last year I rewired an OT 56, which had "failed to ground" either in the harness, or the ignition sw. It was in the owners garage, with the hood up, and he got to the battery disconnect before any more damage occurred. Every wire I removed, dash, engine compartment, even tail lights, had cracked insulation or it cracked when I removed it. This was a nice, well maintained car, from the PNW, so no 100 degree days to speak of. We also found most of the grounds had fairly high resistance, due to surface rust (Seattle? Wet?) even though the floors are good.
If its a restoration, you'll need the correct harnesses. But check all of them, and check the grounds from the tail lights, dash, everything.
My 55 bird has a centec fuse panel, new wiring, and has been no problem for 10 years. The OT car got an American Autowire kit, which was as good as I can imagine. But the 'bird I did custom, from the harness kits. I don't think anyone builds a kit for ford cars of this era.
Yes, I'm a bit paranoid, but I spent 40 years as an electrician, and I haven't burned a building or a ship down, yet.