One possible solution could be to monkey patch the onInspectClick (override Firebug.Inspector.onInspectingClick and call the original after custom logic
But this is rather a hack that could stop working if the internals change (no change is planned but)
Anyway, I would personally concentrate rather on onInspectingMouseUp that is also responsible for calling stopInspecting. Also, we could enhance the current Inspector APIs
(
http://www.softwareishard.com/blog/firebug-tutorial/extending-firebug-inspector-part-x/)
and pass the event object from onInspectingMouseUp to stopInspecting as third argument. Other option could be designing a new inspector callback (e.e. onInspectingMouseUp, that gets the event object)
If you are interested in enhancing the API, please create a new issue report and we can discuss further.
Honza