Response when Web Server is stopped

The response code you're getting (404) is not the proper code for a site that's down - it looks like there's a default IIS-instance that handles the requests when the other instances are stopped. That would also explain why you're not getting a 404 when you stop IIS, since there's nothing left to handle the request.

I assume you're using host headers in IIS?

To handle it properly on the LTM you may want to see if you can disable the default IIS-instance. That way when the specific instance goes down even the standard http-monitor will pick up on it.