Learn English – What’s a word to describe a person being deliberately unclear/obfuscatory

The phrase [being] economical with the truth can have this meaning:

avoiding ​stating the ​true ​facts about a ​situation, or ​lying about it

{Cambridge Dictionaries online}

But dissimulation is a better fit

dissimulation (misleading by withholding pertinent information) {Wikipedia}

I'd avoid the agent noun (dissimulator), which has other connotations (at least) to do with one's beliefs etc, and sounds almost outlandish in any case.

Another term is elliptical:

elliptic or elliptical adj.

3. a. Of or relating to extreme economy of oral or written expression.

b. Marked by deliberate obscurity of style or expression.

{AHDEL} and

3. (Literary & Literary Critical Terms) (of speech, literary style, etc) a. very condensed or concise, often so as to be obscure or ambiguous

{Collins; same link}

I haven't heard of a word that is anywhere near to what you want. But we can be sure of one thing: the action is a stimulus

A stimulus is an energy change registered by the senses, as defined by Wikipedia. Also, it is something causing a response, which is the general meaning we all know.

Have a look at counterpoise from ODO.

(verb) Have an opposing and balancing effect on. (noun) any equal and opposing power or force.

You could say it is a counterpoising stimulus that induces an equal and opposite force or counterpoise.