Test bindings by nested properties through Border.Child and Border.Parent.

BooleanToBrushConverter.cs

[ValueConversion(typeof(bool), typeof(Brush))]
	public class BooleanToBrushConverter : IValueConverter
	{
		public Brush TrueBrush { get; set; } = Brushes.Gray;
		public Brush FalseBrush { get; set; } = Brushes.Gray;

		public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
		{
			return value switch
			{
				true => TrueBrush,
				false => FalseBrush,
				_ => DependencyProperty.UnsetValue
			};
		}

		public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
		{
			throw new NotSupportedException();
		}
	}

BooleanToThicknessConverter.cs

using System;
using System.Globalization;
using System.Windows;
using System.Windows.Data;

[ValueConversion(typeof(bool), typeof(Thickness))]
public class BooleanToThicknessConverter : IValueConverter
{
    public Thickness TrueThickness { get; set; } = new Thickness(0);
    public Thickness FalseThickness { get; set; } = new Thickness(0);

    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        return value switch
        {
            true => TrueThickness,
            false => FalseThickness,
            _ => DependencyProperty.UnsetValue
        };
        throw new NotImplementedException();
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        throw new NotSupportedException();
    }
}

MainWindow.xaml

<Window x:Class="WpfApp.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:local="clr-namespace:WpfApp"
        Title="MainWindow"
        Width="400" Height="300">
    <Window.Resources>
        <local:BooleanToThicknessConverter x:Key="BooleanToThicknessConverterKey" TrueThickness="8" FalseThickness="4"/>
        <local:BooleanToBrushConverter x:Key="BooleanToBrushConverterKey" TrueBrush="Orchid" FalseBrush="Gray"/>
    </Window.Resources>

    <StackPanel>
        <Border BorderThickness="{Binding ElementName=Toggle, Path=IsChecked, Converter={StaticResource BooleanToThicknessConverterKey}}"
                BorderBrush="{Binding RelativeSource={RelativeSource Self}, Path=Child.IsChecked, Converter={StaticResource BooleanToBrushConverterKey}}">
            <Border.Style>
                <Style TargetType="{x:Type Border}">
                    <Setter Property="Background" Value="DarkGray"/>
                    <Style.Triggers>
                        <DataTrigger Binding="{Binding RelativeSource={RelativeSource Self}, Path=Child.IsChecked}" Value="True">
                            <Setter Property="Background" Value="Red"/>
                        </DataTrigger>
                    </Style.Triggers>
                </Style>
            </Border.Style>

            <ToggleButton x:Name="Toggle"
                          Margin="8">

                <Border BorderThickness="{Binding ElementName=Toggle, Path=IsChecked, Converter={StaticResource BooleanToThicknessConverterKey}}"
                        BorderBrush="{Binding RelativeSource={RelativeSource Self}, Path=Parent.IsChecked, Converter={StaticResource BooleanToBrushConverterKey}}">
                    <Border.Style>
                        <Style TargetType="{x:Type Border}">
                            <Setter Property="Background" Value="DarkGray"/>
                            <Style.Triggers>
                                <DataTrigger Binding="{Binding RelativeSource={RelativeSource Self}, Path=Parent.IsChecked}" Value="True">
                                    <Setter Property="Background" Value="Orange"/>
                                </DataTrigger>
                            </Style.Triggers>
                        </Style>
                    </Border.Style>

                    <TextBlock Text="Toggle"/>
                </Border>
            </ToggleButton>
        </Border>
    </StackPanel>
</Window>

The binding through Border.Child does not work while the binding through Border.Parent does.