Wiring Fix Qestion

Hopefully a quick question.

I am pulling apart my 73 Duster and found the multi connector from the ignition switch to the harness is burnt at the red ignition wire and the plastic connector is burnt and turned to dust when I pulled it apart.

Looks like the guy's at the factory left a little bare wire on the ignition wire and over the years it arced and burnt.

Can I just break away the plastic connector, fix the bare wire and then plug all the wires back into each other without the plastic connectorm using the existing pins? I would electrical tape up each wire separately then tape them all together.

Would the wires get too hot for the electrical tape?

Thanks in advance
Brent