Como eu faria um controle entrar / sair quando ele se torna Visível?

Abaixo está minha tentativa falhada:

<code><Window x:Class="WadFileTester.Form1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Name="MyWindow" Title="WAD File SI Checker" Height="386" Width="563" WindowStyle="SingleBorderWindow" DragEnter="Window_DragEnter" DragLeave="Window_DragLeave" DragOver="Window_DragOver" Drop="Window_Drop" AllowDrop="True">
    <Window.Resources>
        <Style TargetType="ListView" x:Key="animatedList">
            <Style.Triggers>
                <DataTrigger Binding="{Binding Visibility}" Value="Visible">
                    <DataTrigger.EnterActions>
                        <BeginStoryboard>
                            <Storyboard>
                                <DoubleAnimation
                                    Storyboard.TargetProperty="Opacity"
                                    From="0.0" To="1.0" Duration="0:0:5"
                                    />
                            </Storyboard>
                        </BeginStoryboard>
                    </DataTrigger.EnterActions>
                    <DataTrigger.ExitActions>
                        <BeginStoryboard>
                            <Storyboard>
                                <DoubleAnimation
                                    Storyboard.TargetProperty="Opacity"
                                    From="1.0" To="0.0" Duration="0:0:5"
                                    />
                            </Storyboard>
                        </BeginStoryboard>
                    </DataTrigger.ExitActions>
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </Window.Resources>
    <Grid>
        <ListView Name="listView1" Style="{StaticResource animatedList}" TabIndex="1" Margin="12,41,12,12" Visibility="Hidden">
        </ListView>
    </Grid>
</Window>
</code>