So the 4 wires in that box are fusible links. One is the main battery feed, one is the alternator, one is the accessory power, and one is the key on power. You can get modern fuses to replace them, as they are prone to failing at this age. The fuses fit perfectly in the stock case. The are FMX style, and I did the conversion for the correct size. They should match the stock link colors, but mine had no wire insulation left when I got it.
I would pull all the fuses and links, and then see if there is still current flowing through the switch. Then add them one by one until it goes away.
Also you can pull the switch off of the key cylinder and clean the contacts. They are famous for going bad, especially the starter ones. I added a relay inline with my key switch. So no power flows through the key switch itself.