The Trickster should have an Archetype as well, because subjective and objective throughlines should be separated. I suppose they could be the Guardian, or the Contagonist.
When you mean Uncontrolled, do you mean Freedom or a Lack of Control? You seem to mean the second ("person who is likely to cause unintentional damage"). If it's the latter then I think Control it could be the Symptom/Focus: the Protagonist and Antagonist desperately try to Control because it reduces their problem (I've read somewhere the Symptom is used by the characters because it actually reduces the problem, but doesn't solve it) AND the Trickster makes everything out of control, which show that Uncontrolled won't solve the problem as well, thus making it the Symptom.
With that line of thinking, both the Protagonist's and Antagonist's pursue of Control and the Trickster's prevention/hinderance of it would be in the encoding of the Element. I think you can assign multiple encodings like those, but I'm not sure if these two encodings are considered as good ones. I'd suggest the Problem to be either Pursue or Avoid.
I'm only guessing, I'm probably totally wrong with the way I took to figure it out. And since there weren't so much infos about it, I assumed a lot of things (Freedom not being the solution, Control being problematic) so it might not be what you're searching for.