I created a console application which will be used by \"Service Broker External Activator\" service. The configuration file in \"C:\\Program Files\\Service Broker\\External
The more likely cause for this is that you are using "localhost" in the ServerName element. I just reproduced it in my working example by changing ServerName to localhost.
The ServerName and the ConnectionString's server MUST be an actual computer name, a machine name specifically, not a DNS name either.
If you make the ConnectionString's server localhost, then nothing will happen after the service starts. You won't get an error, but activation will not occur.