CollectionViewSource in CodeBehind with Template Bindings

Question

I'm creating a lookless control based on Selector in WPF with a Dependency Property named ListItems. When SelectedItems is changed, I do:

// CollectionViewSource ListItems = ...
ListItems.Source = newSelectedItems;
ListItems.Refresh();

And in my ControlTemplate I bind it to a ListBox like this:

<ListBox ItemsSource="{TemplateBinding ListItems}"/>

But no items appear in my ListBox.

I have also tried:

<ListBox ItemsSource="{Binding Source={TemplateBinding ListItems}}"/>

What am I missing here?