Shows how to hook up a button to a view model and update its background color based on logic in the view model.

MvvmButtonBackgroundTest.cs

using System;
using System.ComponentModel;
using System.Windows.Input;
using System.Runtime.CompilerServices;
using Eto.Forms;
using Eto.Drawing;

namespace Test
{
	public class MyViewModel : INotifyPropertyChanged
	{
		public event PropertyChangedEventHandler PropertyChanged;

		static Color DefaultButtonBackgroundColor = new Button().BackgroundColor; // remember default button color

		bool _buttonShouldBeRed;

		Color _buttonBackgroundColor = DefaultButtonBackgroundColor;
		public Color ButtonBackgroundColor
		{
			get { return _buttonBackgroundColor; }
			set
			{
				_buttonBackgroundColor = value;
				TriggerPropertyChanged();
			}
		}

		Command _doSomethingCommand; // change Enabled property of this to automatically enable/disable button
		public ICommand DoSomethingCommand => _doSomethingCommand ?? (_doSomethingCommand = new Command(DoSomething));

		void DoSomething(object sender, EventArgs e)
		{
			_buttonShouldBeRed = !_buttonShouldBeRed;
			ButtonBackgroundColor = _buttonShouldBeRed ? new Color(Colors.Red, 0.2f) : DefaultButtonBackgroundColor;
		}

		protected void TriggerPropertyChanged([CallerMemberName] string memberName = null)
		{
			PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(memberName));
		}
	}

	public class MyDialog : Form
	{
		public MyDialog()
		{
			var button = new Button { Text = "Click Me" };
			button.BindDataContext(c => c.BackgroundColor, (MyViewModel m) => m.ButtonBackgroundColor);
			button.BindDataContext(c => c.Command, (MyViewModel m) => m.DoSomethingCommand);

			Content = new StackLayout
			{
				Spacing = 20,
				Padding = 20,
				Items = {
					"Click the button below",
					button
				}
			};

			this.DataContext = new MyViewModel();
		}
	}
}