In which I realize/remember this specific tab exists... Now that I know of it's existence, what does the Task List do!?

Does it just keep track of the storyline or something?
Is it one of the ways to get gold!? (that might be missions/quests, I dunno)
Is it there for a purpose that was never finished?
Should I even use it?

I have a vague recollection of it being mentioned in the tutorial but I could be wrong.

basically it's the third region's version of the region 1 & 2 quest log- you can pick up tasks from the Ethernian Task Board.

There are four tasks that can be done in the Orchard and three for Astryl's Tranquility.
the board always has four task slots and is refreshed every hour. If you already have a task that would be there in your Log then you can't take it again (as with Missions where if you already have a pet on a specific mission you can't take another of that same mission) until it is no longer in your task log and the hour has rolled again.

It gets gold and probably more importantly it gets you faction points with Ethernia to raise your relationship with the place (which will allow access to more in the shops there)

Oooooh okay, that makes sense, haven't really been into the Third Region much after the LG. Thank Ya :)