The neutral safety switch would not be the cause. The NSS only completes the grounding circuit for the starter relay.
Follow the Battery Positive wire in this
'67 Barracuda Charge/start/ignition diagram.
Everything it is connected to will be at Battery Voltage when the engine is not running, and nothing is turned on. Connections are represented as small circles. The Ammeter internally has a metal plate so is the same as a full time connection.
Do you see that the alternator's output (marked Batt) should read battery voltage when the engine is not running and everything is off?
On the Starter relay;
the thinner brown wire (S4) only sees voltage when the ignition switch is position on Start.
the thicker brown wire (S5) only sees voltage when the starter relay is energized by starter switch (yellow wire) and the NSS being closed.
When the engine is running, everything on those wires should be close to the alternator's output voltage.
Copy the diagram and mark exactly where the voltage is reading 12.5 Voltage
Is there voltage at the alternator output (Batt terminal on the alternator) ?
Maybe its helpful to point out here that Voltage is not power. Voltage only indicates
potential to flow, not that there is any. Its like saying there is 70 psi in the water lines of a house. The pressure indicates water will come out of any faucet that is opened. Taking that further, the current is like the gallons per minute flowing, and power is the combination of pressure and flow (volts and amps in electricity). We can think of the the battery like a cistern or water tank on a roof, and the alternator like a well pump.
If the ammeter's internal plate (shunt) or connections failed completely, there would be no voltage showing on the other side. If it has a poor connection, it will show as a voltage drop when current is flowing. For current to flow, a connection needs to be completed to ground - for example turning on the headlights.
Use an ohmmeter to measure resistance. Best to do this with the battery disconnected.
The ammeter, when functioning, is also a useful tool. It indicates how much current the battery is providing to run the car (discharging) or whether it is being recharged by the alternator.
The fusible link fails mostly due to a short circuit to ground but can also be caused by repeated cumulative damage. See
Fusible Links in Charging Systems with Ammeter
