Searched entire 9.1.1 source and there is no OnActionExecute.
This code is 4 year old and I think it precedes your kind help.
The following is in iextoolbar.pas and relates to a button for text align center.
_AddButton( IELayerTextAlignCenter_Button_ID, TIELayerTextAlignCenter.Create(Self), ITBRES_FORMAT_ALIGN_CENTER_24 );
{ TIELayerTextAlignCenter }
constructor TIELayerTextAlignCenter.Create(AOwner: TComponent);
begin
inherited;
ImageIndex := 80;
fAdjustment := ietaSetAlignment;
fValue := ord( iejLeft );
fActionType := ieaCheckbox;
//
UpdateLanguage();
end;
don't see how button gets clicked ??