Here are a couple of questions to think about.
When you turn off the key, does only the engine keep running, in other words does everything else, radio, fan, lights go off as normally they would?
Where do the wires which power the ignition and the wire which goes to the alternator get close to each other.
Do they share any connectors or components?

I think it is most likely, as Colin UK said, that at some point that wire to the alternator is coming into contact with the wire to the ignition. The wire runs under the front of the engine and then through the firewall to the dash light. The ignition wire runs from the fuse box (does NOT go through a fuse) through the firewall. Along the fire wall to the ballast resistor on the rt of the firewall then back across to the coil and also to the ignition box and to the the starter (terminal 16, and I can't figure what this is for?????)
If your wire harness is bad then anywhere along the firewall there is potential for shorts. Also down at the starter where this wire to terminal 16 could be touching the battery cable to thestarter, In 1983 this wire is brown.

Explore (and a wiring diagram would help)
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744-16v-4+OD 185kmi., 745-16v-4+OD 359kmi., 242Turbo-4+OD 170kmi?, 245DLT automatic 287kmi.