'66 Barracuda having some charging issues

If you want to run a 60 amp alt you should run a new 10 gauge wire from the alt to the starter motor. Then install a volt meter in the car.
By doing this you will get the 60 amp output to the battery without the added resistance of the smaller gauge factory wire and the firewall connector then running through the ammeter to power the car and then back through the firewall connector to the battery.
By not doing this it will be just a short while before the ammeter fails or the firewall connector melts.

The ammeter will then just show how much draw is on the system. Or you could move one wire on the back of the ammeter to the other post bypassing the ammeter so it won't show a discharge.

The reason for bypassing the ammeter is it can't handle 60 amps. When it fails the car won't run until you bypass the meter.