Upgrading wiring harness on 1964 plymouth valiant

Age is not the issue. Its environment and exposure to heat, oil, fuel, etc. Heat can be from engine or from overloading a circuit.
Interiors (Instrument and Body harness) are usually much better condition than engine harness (includes headlights). Wiper motor wires are usually a part of the wiper motor. Some years in particular (early 70s) frequently had leaks onto instrument panel left side so those will have the expected oxidation etc from being wet for extended periods of time.

Common items that will overload circuits are:
New "rebuilt" and similar replacement alternators with high draw rotors (search high draw field current)
Pretty much any headlight but the original 6012 50W/40W lamps.

Common practice that will cause overload of the main power feeds is letting a battery get really low, and then using the alternator to recharge it. If the ammeter is showing over 20 amps charging for more than a minute or so, slow the engine down or turn it off and get a charger.

As far as the alternators go, find a good old one. Certainly in all cases measure the field current draw. its a pretty easy bench test or on the car.

As far as headlights go, if its limited use at night, use good 6012 lamps (or H6024 if not using high beams). Otherwise a headlight relay harness is highly recommended.