Excellent question (viz., ". . . if I do not necessarily agree with the proposal but am arguing for it, with the same goal of making sure it is fully vetted, what am I then?" My answer: You're Socrates (or you are using the Socratic method).
The way you qualify each scenario made me think of Socrates, particularly his way of interacting with someone with whom he was discussing an issue. (By "qualify" I mean your use of qualifiers such as "I may," and "not necessarily.")
As a philosopher and pedagogue, Socrates was on a lifelong quest for truth, and he realized the best way to be a philosopher/pedagogue was to engage people in conversation. Sometimes he would pretend to know less about a subject than he actually did in order to get his interlocutor to say something illogical or inconsistent that he could use as a basis for guiding his interlocutor into the truth.
By the way, we would do well to divest ourselves of the notion that a pedagogue is necessarily dogmatic and unyielding, that he prefers the hortatory approach to discussion as opposed to the give-and-take of the philosophical approach. Good ol' Soc was more interested the abstraction we call truth. His preferred method of arriving at the truth was via dialectic rather than rhetoric. (Think of the dialectic as the art of discussion, and rhetoric as the art of persuasion.)
The two scenarios you describe in your question describe quite well Socrates' modus operandi (M.O). He could play Devil's advocate, hiding his true "feeling" about the subject at hand for the sake of getting his student to think through more thoroughly a proposition that at first blush seems a "no brainer." In effect, he was saying,
"Slow down there, kimosabe (pron. key moe sah' bee). Let's think this through. You may have left a few stones unturned, and your thesis may need a little shoring up in this area or that area. Have you considered the flip side of the coin? It does have some merit to it, does it not? What if I were to introduce the notion of . . .?"
Socrates would have said the above much more subtly and artistically, of course, but in essence his reluctance to barge ahead without first thinking things through (or "vetting" them as you suggest) can be traced to his favored M.O.
By the same token, Soc could ably employ the "opposite" tack in the pursuit of truth by stepping back and exploring more fully the pros and cons of any given position, and not necessarily the better of two options, either. Perhaps a third option exists that no one raised in the discussion thus far, and the best method to arrive at this third option is to vet each of the first two options, first. If neither of them passes muster, Socrates would probably say that time would be better spent on exploring another option.
In conclusion, there may seem to be more than a little disingenuousness (I would call it irony) to Socrates' approach, but we wouldn't be using the phrase "the Socratic method" some 25 centuries after his brief time on earth if there weren't something to commend the method in the scenario you describe.