The "wire" or "resistor" the other answers refer to is typically a pink resistance wire. It should be in a cloth, or woven loom routed with, but separate from, the under dash wiring harness. There will be a short, 4"-6" tail off the ignition switch with a female end that this pink wire plugs into. Sometimes these resistor wires run directly into the firewall plugs and sometimes they plug into another pigtail at the firewall. You can use an ohmmeter to check for continuity before replacing to wire, just to confirm it is the culprit. If it is bad, replace it with the proper wire and route it the way the factory did. As stated above, bypassing this wire will cause premature point's failure. Be sure to disconnect the battery before attempting this repair. Removing the instrument cluster makes the job a bunch easier. It isn't uncommon to see these resistor wires fail in the older Fords

Sources: Ford factory wiring diagrams

Early Mustangs had a voltage dropping resistor (coiled wire type) that was bypassed when in the start position and in series with the coil power wire in the ignition switch run position. If the resistor burned out it simply interrupted the voltage to the ignition coil when released to the run position. I think it was mounted on the firewall in plain sight but that could vary from year to year. Hope that's the problem, it's an easy fix., Les