That would be an ignition coil.
how would you get them apart?they can be repaired if you know what you are doing.
there is no real current so wire diameter is not a real issue. If routed properly, there should be no stress on the connection so it should hold up OK.
Just insulate the connection so it doesn't short to the case.
This is not a first, a few have Soldered/Repaired those broken wires.