Can't fully style a ListBox/Scrollviewer in WPF

this is the part of the template code i got for ScrollViewer using Blend. I added a Rectangle in the bottom right corner and set the Fill to Red. You can style it in the same way or you can expand one of the ScrollBar to cover the space using Grid.RowSpan="2" for VerticalScrollBar(first one) or Grid.ColumnSpan="2" for HorizontalScrollBar(second one).

<Style TargetType="{x:Type ScrollViewer}">
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="{x:Type ScrollViewer}">
                <Grid>
                    <Grid.ColumnDefinitions>
                        <ColumnDefinition/>
                        <ColumnDefinition Width="Auto"/>
                    </Grid.ColumnDefinitions>
                    <Grid.RowDefinitions>
                        <RowDefinition/>
                        <RowDefinition Height="Auto"/>
                    </Grid.RowDefinitions>
                    <ScrollContentPresenter Grid.Column="0"/>
                    <ScrollBar Name="PART_VerticalScrollBar" Grid.Row="0" Grid.Column="1" Value="{TemplateBinding VerticalOffset}" Maximum="{TemplateBinding ScrollableHeight}" ViewportSize="{TemplateBinding ViewportHeight}" Visibility="{TemplateBinding ComputedVerticalScrollBarVisibility}"/>
                    <ScrollBar Name="PART_HorizontalScrollBar" Orientation="Horizontal" Grid.Row="1" Grid.Column="0" Value="{TemplateBinding HorizontalOffset}" Maximum="{TemplateBinding ScrollableWidth}" ViewportSize="{TemplateBinding ViewportWidth}" Visibility="{TemplateBinding ComputedHorizontalScrollBarVisibility}"/>
                    <Rectangle Grid.Row="1" Grid.Column="1" Fill="Red"/>
                </Grid>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>