I've succeed to install the Bluemix Gateway service component as well as to setup the client software at a Linux system, following the "on-premises" scheme.The client is visible in the gateway and I see two green rings confirming the connectivity with a TLS tunnel.
The issue arise when connecting the Bluemix application, a REST consumer that works with HTTPS GET, retrieving data from a REST resource that is located on premises. For this purpose, I've replaced the internal host & domain name, with a simple cloud host name like "abc123" given at the registry of the destination (with no domain) plus aport number :1234, what at the application side gives an address construction of: https://abc123:1234/mypath_to_the_app
I tried to follow the manual which tells:
"Instructions:
In the repository where you are creating your app, when you establish a connection to your on-premises or cloud data, replace the host name and port number with the cloud host name and port number that you were given when you created the destination."
The error displayed at the Bluemix REST application log is "unknown host name".
My Question: What is the correct way to address the "Secure Gatweay" and its destination at the a Bluemix application executing a REST HTTPS GET request? Any further setup required to publish the Secure gateway destination address?
Following the advice posted by @Galen Keene, we were able to circle the issue and solve the problem (see comments above).