You are only half-right. :-k
It is possible that you have a half-bad ignition unit, but you don't have a "CDI". CDI is an entirely different type of ignition system, Suzukis don't have it. Many people mistakenly call any electronic unit a "CDI", but the emphasis there is on "mistakenly".
That is one of the pins that holds a side cover on. Apparently it has broken before, the wire is there as a splint to hold it in place. That wire will help with realignment. Use whatever glue/solvent you have available for ABS plastic. Do you have ABS plumbing there? We use some for drains and/or vents, so solvents and glues are readily available.
A good way to repair ABS parts like the ones Suzuki uses, is to put some Lego bricks in acetone for a few hours; then it can be applied to the part in question and the acetone assures the materials bond together, almost like welding them. I've done that quite a few times with great succes on my GSX 1100 EF. c",)