How to use custom properties in a ControlTemplate trigger

Of course it only takes me 30 minutes after posting my question to find the answer when I spent two days looking for it first. Oh well, the solution is to use DataTriggers.

<ControlTemplate.Triggers>
  <DataTrigger Binding="{Binding RelativeSource={RelativeSource Self}, Path=ThumbIsVisible}" Value="False">
    <Setter TargetName="m_Thumb" Property="Visibility" Value="Hidden" />
  </DataTrigger>
</ControlTemplate.Triggers>

The key is to use the RelativeSource={RelativeSource Self} to find the custom property. After that it works exactly as expected.

It looks like there is an even simpler way to solve this problem.

<ControlTemplate.Triggers>   
  <Trigger Property=local:CustomSlider.ThumbIsVisible" Value="False">     
    <Setter TargetName="m_Thumb" Property="Visibility" Value="Hidden" />
  </Trigger> 
</ControlTemplate.Triggers> 

where local is the namespace of the CustomSlider class.