What would cause it to draw that kind of power with nothing turned on.
A short to ground. The battery can deliver a lot of current; 400 to 600 amps delivered at 12 to 13 volts
The starter is the only item that normally asks for a lot of current.
The ammeter is a link in that circuit.
Yup. In this case, it was not the weakest link. It should have indicated a roughly how much current was flowing before things fried.
So what would be the weak link that would cause that to fry?
It appears in this case the weakest link was the terminal for the alternator wire in the bulkhead connector. In your photo I see nothing remaining there. Several others show some damage. I don't know if that's from this event or previous heat during use. Oxidation, dirt, anything that makes it harder for the electricity to flow creates resistance which creates heat when lots of current tries to go through.
headlight switch, ignition switch, or something with the fusebox.....
Doesn't appear to be unless you find evidence that it went toward one of those.
The wires were cooked to and from the ammeter, but not the ammeter itself.
The ammeter itself is not a problem. Inside are two parallel paths. One small and drives the meter; the other is a big wire called the shunt. Most of the power goes through the shunt. The meter is another link and set of connections. Same deal, they must be clean and snug. As someone mentioned, it would be reasonable to check and make sure it wasn't internally damaged from the current.
edit:
I should also add: after I replaced the wire from the starter relay which was fried (at the time I thought thats all is was), I was able to turn the headlights on and off. The key worked by turning over the starter, but no spark to coil. With the battery connected, the R side park turn signal was on continuously (not blinking) as well as the blinker indicator (also not blinking) on the dash.
If I understand correctly, first the wire from the battery to the starter relay failed.
Then after this was replaced, you were trying to figure out why it would not start. I think this can be figured out. It will help to draw out the wiring to include the voltage regulator and the ignition. I still think its likely alternator or alternator wiring related.
PS. Those Mymopar wiring diagrams didn't seem to quite match what I'm seeing in your photos. Turns out those are not factory diagrams. I have no idea where they got them from - something aftermarket like Chiltons or Mitchels I guess. If its the same as the late 60s, the real diagrams are probably in '71 Plymouth service manual (which is also on that website).
