TMS FNC controls still suffer from the double-click issue, which can be solved by overriding TTMSFNCCustomControl.Capture and removing the inherited call.
Having resolved this, assigning an event handler to the TMS FNC Gantt Chart control's OnDblClick event still won't allow you to handle a double-click.
The reason is, that the FNC Gantt Chart control consists of two sub controls, one for the Gantt list on the left and one for the Gantt Timeline on the right,
so you have to assign the OnDblClick event handler to these sub controls. Unfortunately, both controls can only be accessed by protected properties Tasklist and Timeline.
Now you can either update the TMS FNC Gantt Chart control, declare these properties as public and then assign the event handlers programmatically, or you make the TaskList and TimeLine properties published and have the GanttList control and GanttTimeLine controls explicitly in your .dfm file allowing you assign the event handlers as usual.
This has been fixed and will be available in the next release, normally available by the end of this week.