Change the width of the scrollbars in a scrollviewer on MousOver - wpf

Question

I try to style a ScrollViewer so that the width of the ScrollBar element is changed on a MouseOver. I can style the ScrollViewer and give it an initial width, and it is also possible to change properties on a MouseOver, like the Opacity or Visibility. But I can't change the Width, that property is not changed.
I use this code as an example:
<Style x:Key="myScrollBarStyle" TargetType="{x:Type ScrollBar}">
<Style.Triggers>
<Trigger Property="IsMouseOver" Value="True">
<Setter Property="Opacity" Value="0.9" />
</Trigger>
<Trigger Property="IsMouseOver" Value="False">
<Setter Property="Opacity" Value="0.4" />
</Trigger>
</Style.Triggers>
</Style>
<Style x:Key="myStyle" TargetType="{x:Type ScrollViewer}">
<Setter Property="OverridesDefaultStyle" Value="True" />
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type ScrollViewer}">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="*" />
<ColumnDefinition Width="Auto" />
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition Height="*"/>
<RowDefinition Height="Auto"/>
</Grid.RowDefinitions>
<ScrollContentPresenter Grid.ColumnSpan="2" Grid.RowSpan="2"/>
<ScrollBar
Style="{StaticResource myScrollBarStyle}"
Name="PART_VerticalScrollBar"
Grid.Column="1"
Value="{TemplateBinding VerticalOffset}"
Maximum="{TemplateBinding ScrollableHeight}"
ViewportSize="{TemplateBinding ViewportHeight}"
Visibility="{TemplateBinding ComputedVerticalScrollBarVisibility}" />
<ScrollBar
Style="{StaticResource myScrollBarStyle}"
Name="PART_HorizontalScrollBar"
Orientation="Horizontal"
Grid.Row="1"
Value="{TemplateBinding HorizontalOffset}"
Maximum="{TemplateBinding ScrollableWidth}"
ViewportSize="{TemplateBinding ViewportWidth}"
Visibility="{TemplateBinding ComputedHorizontalScrollBarVisibility}" />
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
Opacity is changed on a MouseOver but if I add a Width, it is ignored. If I look at ControlTemplate.Triggers then I can change the width on MouseOver but that is the width of the complete ScrollViewer, not the ScrollBar element. Even if I point to the element with the targetname PART_VerticalScrollBar.
Searching the internet only results in solutions to change the visibility or opacity, not the width. I could not find any solution.
Is there a solution to do this in a style?