MainWindow.xaml
<Window x:Class="EllipsePropertyChangeDemo.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:EllipsePropertyChangeDemo"        
        mc:Ignorable="d"
        Title="MainWindow" Height="450" Width="800">         
    <Grid >
        <local:EllipseControl Margin="250,0,5,0"   />
        <Button Margin="20" Width="150" Height="40" x:Name="eButton" Content="False" Click="Button_Click" />
    </Grid>
</Window>

MainWindow.xaml.cs
using System.Windows;
using System.Windows.Threading;
using EllipsePropertyChangeDemo;

namespace EllipsePropertyChangeDemo
{
   /// <summary>
   /// Interaction logic for MainWindow.xaml
   /// </summary>
   public partial class MainWindow : Window
   {
	  EllipseViewModel evm = new EllipseViewModel();
	
	  public MainWindow()
	  {
		 InitializeComponent();
		 DataContext = evm;
	  }

	  private void Button_Click(object sender, RoutedEventArgs e)
	  {
		 if (evm.ServerConnected)
		 {
			evm.ServerConnected = false;
			eButton.Content = evm.ServerConnected.ToString();
		 }
		 else
		 {
			evm.ServerConnected = true;
			eButton.Content = evm.ServerConnected.ToString();
		 }

	  }
   }
}

EllipseControl.xaml
<UserControl x:Class="EllipsePropertyChangeDemo.EllipseControl"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" 
             xmlns:local="clr-namespace:EllipsePropertyChangeDemo"             
             HorizontalAlignment="Left" VerticalAlignment="Center" Width="40" Height="40">
    
    <Canvas HorizontalAlignment="Left" VerticalAlignment="Center" Height="35" Width="35" >        
        <Ellipse x:Name="LED" Margin="7"  HorizontalAlignment="Left" VerticalAlignment="Center" Style="{DynamicResource StyleLED}"  />
    </Canvas>
    
</UserControl>

EllipseControl.xaml.cs
using System.Windows.Controls;
using System.ComponentModel;
using System.Windows;
using EllipsePropertyChangeDemo;

namespace EllipsePropertyChangeDemo
{
   /// <summary>
   /// Interaction logic for EllipseControl.xaml
   /// </summary>
   public partial class EllipseControl : UserControl
   {
	  EllipseViewModel evm = new EllipseViewModel();

	  public EllipseControl()
	  {
		 InitializeComponent();
		// evm.PropertyChanged += UpdateLED;
	  }
	  
	  private void UpdateLED (object sender, PropertyChangedEventArgs e)
	  {
		 if (e.Equals(true))
		 {
			this.LED.Style = (Style) App.Current.FindResource("GreenLED");
		 }
	  }
   }
}

EllipseViewModel.cs
using System.Runtime.CompilerServices;
using System.Windows.Controls;
using System.ComponentModel;
using System.Windows;

namespace EllipsePropertyChangeDemo 
{
   public class EllipseViewModel : ObservablePropertyChange // DependencyObject
   {
	  private bool _ServerConnected;

	  public bool ServerConnected
	  {
		 get { return _ServerConnected; }
		 set { if (_ServerConnected != value)
			{
			   _ServerConnected = value;
			   OnPropertyChanged();
			}
		 }
	  }
   }
}

EllipseViewModel.cs
<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
                    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
                    xmlns:local="clr-namespace:EllipsePropertyChangeDemo">
  <Style x:Key="StyleLED" TargetType="{x:Type Ellipse}" >        
        <Setter Property="Height" Value="20" />
        <Setter Property="Width" Value="20" />
        <Setter Property="Stroke" Value="DarkBlue" />
        <Setter Property="StrokeThickness" Value="1" />
        <Setter Property="Fill">
            <Setter.Value>
                <RadialGradientBrush Center="0.3,0.3" Opacity="1">
                    <RadialGradientBrush.GradientStops>
                        <GradientStop Color="LightSalmon" Offset=".05"/>
                        <GradientStop Color="Red" Offset=".95"/>
                    </RadialGradientBrush.GradientStops>
                </RadialGradientBrush>
            </Setter.Value>
        </Setter>
        <Style.Triggers>
            <DataTrigger Binding="{Binding Path=ServerConnected, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" Value="true">                
                <Setter  Property="Fill">
                    <Setter.Value>
                        <RadialGradientBrush Center="0.3,0.3" Opacity="1">
                            <RadialGradientBrush.GradientStops>
                                <GradientStop Color="LightGreen" Offset=".05"/>
                                <GradientStop Color="Green" Offset=".95"/>
                            </RadialGradientBrush.GradientStops>
                        </RadialGradientBrush>
                    </Setter.Value>
                </Setter>
            </DataTrigger>
        </Style.Triggers>
    </Style>
</ResourceDictionary>

ObservablePropertyChange.cs
using System.ComponentModel;
using System.Runtime.CompilerServices;

namespace EllipsePropertyChangeDemo
{
   public class ObservablePropertyChange : INotifyPropertyChanged
   {
	  public event PropertyChangedEventHandler PropertyChanged;

	  internal void OnPropertyChanged([CallerMemberName] string propertyName = "")
	  {
		 PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
		 
	  }
   }
}

App.xaml
<Application x:Class="EllipsePropertyChangeDemo.App"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:local="clr-namespace:EllipsePropertyChangeDemo"
             StartupUri="MainWindow.xaml">
    <Application.Resources>
        <ResourceDictionary>
            <ResourceDictionary.MergedDictionaries>
                <ResourceDictionary Source="/EllipseStyle.xaml"/>
            </ResourceDictionary.MergedDictionaries>
        </ResourceDictionary>
         
    </Application.Resources>
</Application>