I'm guessing this is why I keep getting this wrong. Somehow, I started equating the structure of "Táim go dona," = I am bad, with this, and have endlessly tried to make this "Tá scéal éifeachtach." I think that I need the copula when the pronoun is being equated to a noun with an adjective. In "Táim go dona," the pronoun is being equated to the descriptor, with no noun. Is this heading in the right direction?
Yes. In Táim go dona, mé is the subject and go dona is a predicative adjective, so that sentence uses bí rather than is. In this exercise, é is the subject and scéal éifeachtach is a predicate complement, so it uses is rather than bí. (The same would apply even if éifeachtach weren’t there.) If scéal weren’t there, then it would be Tá sé éifeachtach instead.
is can be pronounced “ish” before pronouns that begin with a slender vowel, but it isn't required. is é, is í and is iad are often pronounced iss
Here's another example from a completely different source:
Click on Audio 2, then select Track 20
This audio is from Routledge's Colloquial Irish. The 3rd and 4 lines of the dialogue are:
Is é Mícheál an craoltóir.
Is é an craoltóir é.
The first line is pronounced "iss ay", the second is pronounced "shay".
(There are some other examples in the audio from that book, but that particular example includes both pronunciations in a fairly unambiguous manner).
The sentence Is scéal éifeachtach é is a copula, linking two nouns (or, in this case, a noun and a pronoun). The nouns being linked are scéal and é - "story" and "it". In English, we put the pronoun first - "It is a story".
éifeachtach is just an adjective, describing the type of story, so we get "It is an effective story".
"The story is effective" only has one noun ("story"), and "effective" is still just an adjective, so we just use the verb bí in Irish - tá an scéal éifeachtach.
Note that while the teanglann.ie website is funded by Foras na Gaeilge, the Foclóir Gaeilge-Béarla section of that site is an electronic representation of a dictionary that was first published in 1977, and is generally referred to as the FGB or Ó Dónaill.
The FGB was published by An Gúm, which became part of Foras na Gaeilge when Foras na Gaeilge was created in the late 90's.