I'm not surprised the wiring is knackered if it's 1779 vintage!
If you are doing a complete rewire, I suggest you use modern "thin wall" wire. You can also take the opportunity to move the fusebox into the cabin, out of the weather. There is room under the passenger side dash. Use similar wire sizes to the original, the thin wall stuff has a higher current rating so you should be safe with that strategy.
I have done a partial rewire, using an Uno Turbo loom and fusebox I happened to have, combined with the original HPE rear loom. If you are keen to save money and effort, you could do something similar with a complete second hand loom from a Punto or or other Fiat of similar size to the Beta.
You do need to be able to read and understand wiring diagrams too!
Cheers R
