On_Button_Press_Event in Text_View

Using gtkada (gtk3), is it possible to use a custom handler to
deal with a button-press-event (or other events if necessary)
inside a widget such as a Text_View?

For example I create a Text_View with buffer. To process a
button-press within that view I have this code in my main
procedure:

  The_View.On_Button_Press_Event (Press_CB'Access);
  The_View.Set_Events (The_View.Get_Events or Button_Press_Mask);

The callback looks like this:

  function Press_CB (Self  : access Gtk_Widget_Record'Class;
                     Event : Gdk_Event_Button)
                     return Boolean is
   begin
      Put_Line ("Mouse click in text view");
      return True;
   end Press_CB;

So far, so good.

But I'd like to pass additional data to the callback,
without using global variables/records if it can be
avoided.

I have a custom handler used when I update the Text_Buffer:

 Button_Callback.Connect
   (Update_Button, "clicked", Update_Clicked'Access,
    Buffer_To_Pass);

That works fine so I was imagining something similar might
be possible, but I've run through various permuations of
records and access types but not yet got a working callback.

Any help gratefully received (I can post the full code if
that's useful).

Kind regards,

Gavin McCord