"Pulsing" voltage, RPM drop with load.

Using Dana's car as an example.
With no current flowing. Voltage was 12.5 V at the battery, and should be the same at the alternator, key switch feed, etc.
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The battery voltage drops when loads are applied. The headlights, parking and brake lights is roughly a 12-15 amp draw.

If the connections were perfect, the inside measurements should have been the same as the battery voltage during those tests.
Lets look at the heaviest loads.
With the headlights on, engine off, there was a 0.9 Volt drop with the lights on and brake applied.
Because we know the path the current is flowing, we can deduce the voltage drop was between the battery and the fusebox. This assumes the ground connection is not contributing to the drop. But it is not surprising there would be some resistance in 52 year old wiring connections.
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Engine running, current flows the other way.
The voltage at the alternator and battery should have been same as measured inside. But knowing there is some resistance in the wiring, there probably was a drop in voltage between the alternator and the battery.
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All this is an aside from the fact that alternator's capacity increases with rpm.
When Dana measured 13.3 volts with the headlights on, that is typical of alternators getting maxed out at idle.
A check at the alternator output terminal would confirm this.

When the engine speed is at 1250 rpm, the alternator should easily supply lights including brake lights, plus heater fan or wipers.