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You're going to have to cut it anyway to make a connection. Your pic with the starter in it makes me think that the red wire is the fusible link and it should be on the starter big terminal that's the one that will be feeding power to the ignition switch. The purple one probably broke off of the S terminal, a small terminal. I'd go ahead and put a ring terminal on that one and it should have power from the ignition switch start position if the ignition switch is getting power from the red one at the starter.
Could the "plastic portion" be the identifier/label showing the value of a fusible link, does it have a number on it?