Is there a specific name for an intentionally trivial or flippant answer that is designed to elicit a necessary clarification in a question?

Solution 1:

Will you take a four-word phrase?

When you respond with these flippant assumptions of the context for the vague remark, you are

shooting in the dark

Here's a definition of a shot in the dark:

an attempt to guess something when you have no information or knowledge about the subject and therefore cannot possibly know what the answer is

from the from the Cambridge Advanced Learner's Dictionary & Thesaurus, Cambridge University Press

Solution 2:

Rhetorical device. I was thinking about whether "talking things to it's logical extreme" was appropriate and looking it up on Wikipedia which led me to Rhetorical device which is described as a technique that a speaker uses to convey to the listener a meaning with the goal of persuading him or her towards considering a topic from a different perspective.

i.e. by asking absurd follow-up questions you ask the other person to consider their initial question from your point of view and thus clarify their point.

"I can't get my suitcase in the car"
"Have your arms fallen off?"
"No."
"Has the car been stolen?"
"No, it's too heavy, will you help me?"