I have cleared both these islands numerous times. A Tegi has never spawned. I know others who have cleared these islands multiple times and a Tegi has never spawned. I suspect the actual location for a Tegi spawn is the "secret" area through the tunnel. It's a lot harder, compared to these islands.
Replying to my own post. The mob, at least on the mac Al'Kabor server, is not named a Tegi Cohort. He is a Vas Ren Cohort, a rare spawn. I've gotten the leggings to drop but not the flamberge.
Tegi Cohort spawns on one of the 2 islands where the Grol Baku and Vas Ren co-exist. These two islands are in the NW corner of the zone across from the Elemental Island. You can either get your swimming skill up while swimming there or run the outer edge of the zone to get to it. The Tegi Cohort drops 2 items that I know of, Gray Leggings and the Cohort’s Flamberge, which is the more rare of the two.
Besides the Tegi Cohort there is a Tegi Leader, a Tegi Priest and a Tegi Taskmaster that also spawns there. The Tegi Priest drops a nice hammer, the Taskmaster the Taskmaster's Whip and the Tegi Leader the Tegi Leader's Blade.
There is a combination of 18 Vas Ren and Grol Baku on the island. I have not been able to determine if there is a specific spawn time or a placeholder. I have tried killing everything on the islands to see if it would spawn them. I have also checked the times. They just seem to be random. I have also noticed that some times the same named Tegi would spawn twice in a row then other times not. So it is really hard to say what causes them to spawn.
If there are any shaman Vas Ren or Grol Baku around when your fighting take them out first, they heal the others.
I was a 40th level Ranger when I obtained mine and most of them were green to me. There where a few light blue and the occasional dark blue. I think I went up 1 blue in 4 hours.
So I hope this helps. There are some pretty nice items dropping in Twilight Sea but rarely anyone camping.