How do I add a TraceListener so that it listens to Trace.WriteLine?

Given this code:

 using UnityEngine;
 using System.Collections;
 using System.Diagnostics;
 public class TestTrace : MonoBehaviour {
     void Start () 
     {
         TextWriterTraceListener myListener = new TextWriterTraceListener("TextWriterOutput.log", "myListener");
 
         Trace.Listeners.Add(myListener);
         Trace.WriteLine("Output via Trace.");
         Trace.Flush();
 
         myListener.WriteLine("Output direct from listener.");
         myListener.Flush();
     }
     
 }
 

The given output to the trace file is:

Output direct from listener.

when I would expect:

Output direct from listener.
Output via Trace.

What am I doing wrong?