// This is the animation method, it is called from the
// SelectionChanged handler in the behavior passing the
// AssociatedObject as the ComboBox parameter.
public void AnimateComboBox(ComboBox cbo)
{
    LinearGradientBrush myBrush = new LinearGradientBrush();
    myBrush = (cbo.BorderBrush as LinearGradientBrush);

    Storyboard sb = new Storyboard();
    sb.Duration = new Duration(TimeSpan.FromMilliseconds(3000));

    //have to animate each gradient stop
    foreach(GradientStop s in myBrush.GradientStops)
    {
        ColorAnimation anim = new ColorAnimation();
        anim.To = Colors.Red;
        anim.Duration = new Duration(TimeSpan.FromSeconds(0.5));
        //auto-reverse and repeat for pulsation
        anim.AutoReverse = true;
        anim.RepeatBehavior = RepeatBehavior.Forever;

        Storyboard.SetTarget(anim, s);
        Storyboard.SetTargetProperty(anim,
            new PropertyPath(GradientStop.ColorProperty));

        sb.Children.Add(anim);
    }

    sb.Begin();
}

<ComboBox > <!-- leaving out ItemsSource and so-forth for brevity -->
    <i:Interaction.Behaviors>
        <vms:AnimateSelectionChangedBehavior/>
    </i:Interaction.Behaviors>
</ComboBox>
<ComboBox>
    <!-- this one does not have the behavior, but its border
        changes with the other one. -->
</ComboBox>