I would examine all of the connecting points for the J2 wire and both power feeds (R6, A1). The shop manual will show where those wires connect.*
I'd also remove the alternator for closer examination. Fortunately all of the parts are pretty easy to access and replace on a squareback. If the rotor is not damaged the replacing parts is easy and it will be better than what is sold over the counter. If you have a multimeter, check each field terminal to be sure they are not connecting to ground. We can go into depth later. its in the shop manual too.
Did it go up in smoke when the new battery was installed or when the engine was running?
These are the questions that have to be answered to track down the fault.
I'm going to assume you did not look at the ammeter, labelled"alternator". If it had been pointing to charge, I'd suspect high or uncontrolled voltage, and if it was showing discharge, then a short and/or alternator failure.
Since you're new to this, lets start here.
Take your finger or mouse pointer and follow the wire from the battery positive to the key switch.
View attachment 1716221278
Everything connected to that line is electrically hot. When the key is run, as shown in the diagram, then ignition wire is hot.
If it the short was in that circuit, it should have only occurred when the key was turned to run.
When the engine is running, power comes from the alternator down the R6 wire. Take your pointer and follow that to the main splice (black circle). Then it goes to the key switch along the J1 wire. If the battery needs recharging, some current will also flow to it and the ammeter will show charging.
Now lets go to the "ignition run" wire. The J2 wire connection at the voltage regulator is for sensing only. The power to create the alternator's electromagnetic field goes through the J2 wire to the alternator, and then out through the R3 wire. The regulator connects the R3 wire to ground. The VR switches the connection on and off as needed to maintain 14.2 Volts.
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* How to use the wiring diagram from the shop manual.
Example. We want to know about the condition of J2 at the bulkhead connection.
Here's the connector.
View attachment 1716221286
On the engine wiring diagram, follow wire J2 back to the connector.
View attachment 1716221288
The leads to position 23 on the connector.
Electric choke. Just look for electric wires going to either side of the carburetor. if so, we'll come to this.