Yes you need to trouble shoot this, but to do so you need to have a plan and understand the circuits.

Go to the function diagrams in my first post.
Then make a wire diagram for your car and identify places you can access to isolate sections of the circuit. Feel free to use the modify the wire diagram at the bottom of the page to create one for your 70 E.

The functional diagram will make it easier to see that the fusible link only protects against high current from the battery or extreme charging of a dead battery.

In addition to the possibilty of a short to ground, it is possible that your alternator is failing, that the pertronix has been wired to battery side of the charge circuit, or the pertronix is draining the battery more during start up than the points system. ---> The lower the battery's charge, the more current the alternator will supply through the fusible link. The fusible link can handle 40 to 60 amps depending on vehicle, at least for a few minutes.