Is "there has not been" in the passive voice?

Your sentences is not in the least bit “passive”. To show you what a passive version would be, we will posit that:

1. To storm something is the transitive verb that acts upon something, as in storming the beaches of Normandy.
2. Cyclones is the grammatical agent directing that action.
3. Tahiti is the grammatical patient being acted upon by that action.

Then it follows that this is the active way to express that relationship:

• Cyclones haven't stormed Tahiti for twelve years now.

While this is the passive way to express that same relationship:

• Tahiti has not been stormed by cyclones for twelve years now.

In both versions, the agent and patient are the same even though the subject and object have been swapped.

No one seems to know what passive means any longer. Please read linguist Geoffrey Pullum’s brief synopsis of the passive in English. He also has a longer paper on this if you'd like more details.

Take a look at the following progression.

1. In Tahiti, there is a cyclone. [In the active]
2. In Tahiti, there is not a cyclone. [In the negative but in the active still]
3. In Tahiti, there has not been a cyclone. [In the active past perfect]
4. In Tahiti, there has not been a cyclone for 12 years. [In the active, still]

Rephrased, it is as follows.

• There has not been a cyclone in Tahiti in 12 years.

In passive voice, the verb is generally the copula ("be"), and the "true" subject follows the verb. For instance, in "The book was found by the student", grammatically the subject is "the book", but since the student is who actually performed the action, there is some sense that they are the "true" subject.

In your sentence, there is a form of "to be", and the subject comes after it. This may have caused you to think that this fits the pattern of the passive voice. However, in the passive voice, the copula is the main verb and is followed by a participle, but here the main verb is "have", and the copula is the participle.

The reason that the "true" subject follows the verb is because there is a dummy subject. We have a situation where we are declaring that the subject does not exist (the subject is a cyclone in Tahiti, but we're declaring there is no such cyclone), so it would be confusing to say "A cyclone has not been in Tahiti" (the phrase "a cyclone" has nothing to refer to). If we phrased it that way, it could easily be interpreted as saying that there is a cyclone, and it was somewhere other than Tahiti. We use the dummy subject to discuss the existence of the "true" subject, rather than use something whose existence is being denied as the grammatical subject.

No, "In Tahiti there has not been a cyclone for 12 years" is not passive.

I believe it follows the syntax rule for passive voice: to be + past participle

The passive voice is usually formed with a form of to be, along with the past participle form of another verb. "Been" is the past participle of be, so your sentence doesn't meet the criteria of that rule: it only has a form of to be, but no past participle after that form. A passive sentence would have a past participle after the form of to be, like this: "The cookies have been eaten". Here been is the form of "to be" (it happens to be the past participle form, but that's not related to the sentence being passive) and "eaten" is the past participle that makes the sentence passive.

"There has been" is simply "There is" put into the perfect construction: a form of have + past participle). "There is" is not a passive construction, so "There has been" isn't either (compare the non-passive "They have eaten (the cookies)").