How can I test a class that uses DispatcherTimer?

I've found a couple of Stack Overflow questions along with a couple of blog posts that already touch on this topic, but unfortunately none of them are meeting my needs. I'll just start with some sample code to show what I'd like to accomplish.

using System;
using System.Security.Permissions;
using System.Threading.Tasks;
using System.Windows.Threading;
using Microsoft.VisualStudio.TestTools.UnitTesting;

namespace MyApp
{
    [TestClass]
    public class MyTests
    {
        private int _value;

        [TestMethod]
        public async Task TimerTest()
        {
            _value = 0;
            var timer = new DispatcherTimer {Interval = TimeSpan.FromMilliseconds(10)};
            timer.Tick += IncrementValue;
            timer.Start();

            await Task.Delay(15);
            DispatcherUtils.DoEvents();
            Assert.AreNotEqual(0, _value);
        }

        private void IncrementValue(object sender, EventArgs e)
        {
            _value++;
        } 
    }

    internal class DispatcherUtils
    {
        [SecurityPermission(SecurityAction.Demand, Flags = SecurityPermissionFlag.UnmanagedCode)]
        public static void DoEvents()
        {
            var frame = new DispatcherFrame();
            Dispatcher.CurrentDispatcher.BeginInvoke(DispatcherPriority.Background, new DispatcherOperationCallback(ExitFrame), frame);
            Dispatcher.PushFrame(frame);
        }

        private static object ExitFrame(object frame)
        {
            ((DispatcherFrame)frame).Continue = false;
            return null;
        }
    }
}

This code works fine if, instead of using a DispatcherTimer, I use an ordinary Timer. But DispatcherTimer never fires. What am I missing? What do I need to get it to fire?