Even though the XML documentation says use FindName instead, that doen't work when inside OnApplyTemplate(). Here I was trying to reference a PART_ slider in a custom control.
Here is a sample XAML that will cause FindNames to fail and return Null:
<Window.Resources>
<ControlTemplate x:Key="FancyColorPickerTemplate">
<Border Background="LightBlue"
BorderBrush="LightSeaGreen"
BorderThickness="1">
<Grid>
<Grid.RowDefinitions>
<RowDefinition></RowDefinition>
<RowDefinition Height="Auto"></RowDefinition>
</Grid.RowDefinitions>
<Grid.ColumnDefinitions>
<ColumnDefinition></ColumnDefinition>
<ColumnDefinition Width="Auto"></ColumnDefinition>
<ColumnDefinition Width="Auto"></ColumnDefinition>
<ColumnDefinition Width="Auto"></ColumnDefinition>
</Grid.ColumnDefinitions>
<Grid.Resources>
<Style TargetType="{x:Type Slider}">
<Setter Property="Orientation" Value="Vertical"></Setter>
<Setter Property="TickPlacement" Value="TopLeft"></Setter>
<Setter Property="TickFrequency" Value="50"></Setter>
<Setter Property="Minimum" Value="0"></Setter>
<Setter Property="Maximum" Value="255"></Setter>
<Setter Property="Margin" Value="5"></Setter>
</Style>
<Style TargetType="{x:Type TextBlock}">
<Setter Property="Margin" Value="3"></Setter>
<Setter Property="FontSize" Value="10"></Setter>
</Style>
</Grid.Resources>
<Ellipse Grid.Column="0" Grid.RowSpan="2"
Margin="10" Height="120" Stroke="LightGray" StrokeThickness="5">
<Ellipse.Fill>
<SolidColorBrush Color="{Binding Path=Color,
RelativeSource={RelativeSource TemplatedParent}}"></SolidColorBrush>
</Ellipse.Fill>
</Ellipse>
<Slider Name="PART_RedSlider" Grid.Column="1"></Slider>
<TextBlock Grid.Row="1" Grid.Column="1">RED</TextBlock>
<Slider Name="PART_GreenSlider" Grid.Column="2"></Slider>
<TextBlock Grid.Row="1" Grid.Column="2">GREEN</TextBlock>
<Slider Name="PART_BlueSlider" Grid.Column="3"></Slider>
<TextBlock Grid.Row="1" Grid.Column="3">BLUE</TextBlock>
</Grid>
</Border>
</ControlTemplate>
</Window.Resources>