Symptoms

When editing an application link (Administration > Application Links and then select the "Edit" link) the only one authentication type that appears for either Outgoing Authentication or Incoming Authentication is the OAuth tab. This is opposed to seeing all three tabs: Trusted Applications, OAuth, Basic Access

Cause

The logged in user only has "Admin" privileges.

 

Resolution

Log in with a user that has "System Admin" privileges or have a user with "System Administrator privileges" grant your user this role via Global permissions.