The Wait is Over
If you have the Summoner job, there's one more thing you can do before boarding the Skyhold. Jump aboard the Rubadub and make your way to Gravemark Village in the Eternia region. From here, travel a short distance north-east and land in the small inland sea.
Approach the shallow waters towards the east until the Rubadub can go no further. Next, tap the Rubadub icon on the map menu and select the bottom-most option to board the rowboat. While on the rowboat, follow the watery path south towards dry land.
After disembarking, march to the north-most edge of the island to encounter the final, elusive Anchorite as hinted in Mephilia's Memos. As with all Anchorite encounters, be sure to save before accepting the ordeal. Also, while you're here, try refusing the ordeal to tease the Anchorite...
Boss: Anchorite of Light
The Anchorite can cast Comet to rain 1-4 non-elemental hits on one or Meteor to unleash 4 powerful non-elemental hits on random party members. Like before, buffing your magic defence and/or dropping the Anchorite's magic attack with a Pirate are both good survival options.
Occasionally, it may cast Stop to try and freeze a party member, preventing them from acting for a few turns. Unlike most ailments, it cannot be cured with healing spells or items, but rather the Exorcist's Purgation. Or you can prevent it with the Time Mage's Stop Immunity.
Every so often, the Anchorite will cast Amaterasu on itself to restore 9999 HP. Like other Summon Magic, it cannot be reflected. If you want, use the Exorcist's Undo HP to revert the Anchorite's HP, but generally you should be OK so long as you deal enough damage.
Unlike its deathly counterpart, the Anchorite of Light has relatively mediocre physical defence and a weakness to the Dark element, so you can incorporate those into your strategies. For instance, sword attacks infused with the Hawkeye's Darkhead are sure to leave a mark.