THANK YOU! THANK YOU!

I just replaced my turn signal (multi-switch) and part of the documented process was to pull ignition cylinder. I knew my chime was related to that, but your post took me right to the problem. Awesome!

 

Regarding, "used a plastic tie-wrap around the outside of it and the lock barrel to hold it in place permanently. "

This was a very helpful suggestion for me.
Here is my fix.

...used a plastic tie-wrap around the outside of it and the lock barrel to hold it in place permanently.