Test that task is being awaited

I have the following code which i'd like to test:

private Task _keepAliveTask; // get's assigned by object initializer

public async Task EndSession()
{
    _cancellationTokenSource.Cancel(); // cancels the _keepAliveTask
    await _logOutCommand.LogOutIfPossible();
    await _keepAliveTask;
}

It is important that the EndSession Task only ends once the `_keepAliveTask' ended. However, i'm struggling to find a way to test it reliably.

non-async method

If there wouldn't be the call to _logOutCommand.LogOutIfPossible() it would be quite simple: i'd just remove the async and return _keepAliveTask instead of awaiting it:

public Task EndSession()
{
    _cancellationTokenSource.Cancel();
    return _keepAliveTask;
}

non-async method, sync over async

Of course, i could do something similar:

public Task EndSession()
{
    _cancellationTokenSource.Cancel(); // cancels the _keepAliveTask
    _logOutCommand.LogOutIfPossible().Wait();
    return _keepAliveTask;
}

But that is a no-go (sync over async).

observing effects instead of verifying calls

Now of course instead of "unit" testing method calls etc. i could always observe effects. Which is: As long as _keepAliveTask hasn't ended the EndSession Task mustn't end either. But since i can't wait indefinite one has to settle for a timeout. The tests should be fast so a timeout like 5 seconds is a no go. So what i've done is:

[Test]
public void EndSession_MustWaitForKeepAliveTaskToEnd()
{
    var keepAlive = new TaskCompletionSource<bool>();
    _cancelableLoopingTaskFactory
        .Setup(x => x.Start(It.IsAny<ICancelableLoopStep>(), It.IsAny<CancellationToken>()))
        .Returns(keepAlive.Task);

    _testee.StartSendingKeepAlive();

    _testee.EndSession()
            .Wait(TimeSpan.FromMilliseconds(20))
            .Should().BeFalse();
}

But i really really dislike this approach. It's hard to understand and it's unreliable.

So is there any reliable way to verify that an async method is awaiting a task?