I just recently returned from a course where we utilized a static rope to construct a top-rope anchor from a top-accessed ledge: the system was like that described in this answer - the resulting configuration of the rope being a "V" with an additional line running from one of the apexes turning the static configuration into an "N".
The actual anchor legs are accomplishable via a number of means; however, when establishing the instructor tether, I am unsure of what knot is acceptable when going over the ledge and transferring to the pre-setup rappel.
Typically, one leg is wrapped around a tree (I climb in the Southeast) and is secured with a Bowline (not enough for a tail). The length of the rope is run down to ledge and back to another anchor point (in this case a tree), creating the "V".
What I've typically done is used doubled cordellete around the tree (redundancy) with an Overhand on a Bight. A locking carabiner is put through that Bight and the final leg is tied to that using a clove hitch.
Is it appropriate to use the tail (on the right; as an example) of the adjustable hitch for my instructor tether? If not, how would you configure your use of the natural anchors to provide you with a tether for managing the site?