Argh. Too much bad info from the 'net and earlier myths.
Chrysler actually knew how to build cars in spite of all the experts who think otherwise.
Sorry for the rant, but we've all been caught up in this stuff so its not directed at you, but the situation in general.
Lets break this up.
New and 12.4 Volts means its not charged. Voltage alone is only a clue too the state of charge (how much energy it has stored), but 12.4 volts is low.
The alternator output capacity following the rpm is normal for an alternator. BUT and its a big BUT, your bits of info tell us more.
1. The fact it stays around 14 volts at higher rpms (doesn't continue to climb with rpm) indicates the regulator is working.
2. Low voltage at slow idle means the alternator is maxed out or the field current is too weak. Once the battery is recharged, the only loads at idle should be ignition and alternator field. Thats 5-6 amps with a corrent alternator and maybe 10 amps with a replacement alternator that has a low resistance/high draw rotor in it.
Your volt meter should not be getting hot. It should not be in the circuit where the ammeter was. It should be connected to a switched circuit (can tap in on the switched portion of the fusebox).
If the voltmeter is located currently, then it would be worth checking for resistance using voltage drop method.
First. Charge the battery on a charger. If you have to buy a charger, so be it. Make sure it can do a slow charge (2 or 3 amps).
Voltage comparisons can be made between any point and ground. Or between two points (as illustrated below).
Either way, current must be flowing (electrons moving) for there to be a voltage drop through resistance. No current, no drop. = test invalid.
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Here's an example of checking for resistance betweenthe battery and the mainsplice
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Checking for resistance between the battery positive and the mainsplice using two measurements to ground.
This method will also include votlage differences (resistance) in the grounding.
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