Specifically meaning what?
Did the radio work with the ignition switch off, run or accessory?
Was this when you turned the key to Run or to Start?
The answer to which position the switch was will help you identify which circuit grounded out.
When a fusible link burns like that, it is because the battery found a direct path to ground.
On a stock '72 A-body the begining of that path would be as gary mentioned.
It's the Battery feed/charge wiring to the main splice, and in your instance to the ignition switch. The grounding had to be a wire after the ignition switch .
Some simplified illustrations here.
Fusible Links in Charging Systems with Ammeter