Reader response v. authors intent
Meaning:
An old conundrum. Is it (meaning) controlled by authors intent?
Actually, there is no conundrum.
Meaning is not controlled by intent alone—there is no control over meaning except what is ascribed by law (and laws can be changed). This is amply demonstrated in the field of literature and criticism, but also in law. If someone writes a contract and phrases it so that it actually (according to English grammar and spelling, for instance) says something different than the author intended, and the signer demonstrates they understood the contract as written, then the courts (according to what I've been told by my graduate school professor who used to testify in court regarding the grammatical wording of contracts) go along with the grammar rather than the supposed intent.
Pictorial symbolism, except in things like traffic signs, etc., has far less "control." And once the intender is dead, it's all open to interpretation.
Nevertheless, an attempt to learn what was intended or understood at the time of creation is almost always worthwhile and enlightening and can expand our understanding of the creator, the period, the development of human ideas, etc.
In some forms of art and communication, intent and purpose is never conceived of as a static thing, but rather as a continuing dialog or dance between the work itself and those who experience it. It's part of what makes art into "art."
Re: ambiguous symbolism:
does the author then have the right to say in regards to any response: that is not what is meant or intended? (Of course, they may say, that is not what
I meant or intended.)
Authorial intent or thinking is not communicated through Cymbals
As you note, an author can and will say whatever they want to say. In art, once a work is made public it no longer belongs (in terms of meaning and what it expresses) to the creator. Rather all meaning exists in the observer/experiencer.
Added: Humanity is made all the richer for the many and great variety of interpretations of Shakespeare.