type
  TMainForm = class(TForm)
    TrayIcon: TTrayIcon;
    {...}
    procedure TrayIconClick(Sender: TObject);
  end;

var
  MainForm: TMainForm;

implementation

type
  THackCustomTrayIcon = class(TCustomTrayIcon)
  end;

procedure TMainForm.TrayIconClick(Sender: TObject);
var
  M: TMessage;
begin
   M.Msg := WM_SYSTEM_TRAY_MESSAGE;
   M.LParam := WM_RBUTTONUP;
   THackCustomTrayIcon(TrayIcon).WindowProc(M);
end;