TF31003 error message when connecting to On-Premise TFS via Https

I was working on a project where we recently discovered a defect with Visual Studio 2013 and connectivity to TFS when connecting to TFS via Https:

If you connect to TFS by selecting the Https radio button AFTER entering the TFS Url, your connection will FAIL!!

However, if you select the Https radio button FIRST, the connection succeeds!

You can further verify that this is the root cause of the defect by simply connecting to TFS Web Access in the browser:
https://<TFS Url>/tfs/DefaultCollection

If the connection succeeds using the same login credentials, the defect lies in connectivity via Visual Studio.

This essentially becomes an "order of operations" defect inherent from the design of the User Interface in Visual Studio.

Therefore, to avoid this problem when connecting to TFS via Https, follow these steps:

1. Select the Https radio button BEFORE entering any TFS Url information
2. Enter the TFS Url
3. Attempt to connect to TFS via login credentials
4. Verify that the login succeeds

This has also been filed as this Microsoft Connect feedback item: https://connect.microsoft.com/VisualStudio/feedback/details/1443294/tfs-connectivity-order-of-operations-for-https

If you also experience this issue, please vote on this Microsoft Connect item to ensure that Microsoft fixes this major defect in the next release of Visual Studio 2015/Team Foundation Server 2015!!