In addition, there were some users that I could not add the application as it was grayed out.
The fix for this one was to make the user a Call Agent User Type.
To work around the issue reported, I created a new group; added the application and permissions to this group. I then added a user into the group. The result was that the user did not see the application.
Fix for that one was to add the application to the user (grants permission to the application). Then the settings within the User Group for that application took effect.
In summary, add the application to the user. Add the application to a User Group with the respective permissions. Then add the user to the user group. Somewhat streamlines the process rather than having to set permissions for each user individually.