Duster fusible link wiring problem

It will help you understand why AJ posted that once you understand the main circuits are always hot. No current flows in those wires when the switches are off, but the potential is there. So you just need to figure out what is completing the circuit to ground when hooking up the battery. If the key is off, headlights are off, then it really limits the possibilities. Current is flowing, and it shouldn't be. If the fusible link is not compromised (and it may be from your previous posts) then getting hot indicates a lot of current.

Read this so you understand how a fusible link protects the unfused wires.
Fusible Links in Charging Systems with Ammeter
Shown there is a basic circuit with one fusible link. Once you understand how it works, you can make a similar diagram for your car. This will help you find the short.

If the diagram here is to be believed, your Duster has two fusible links. Knowing which one (or both) are getting hot will narrow the problem. If that wiring diagram is correct, the power is distributed from two points instead of one main splice used in earlier years. The wire to the ignition switch is spliced in on the engine compartment side and gets its own fusible link. Thats one reason why it looks different than what we typically see here.
(A factory shop manual diagram is better to rely on than the one in that link. But if it matches what you have in the car, that's great.)