First, note that "x is y" is not always logically equivalent to "y is x". For example, "Fools are my friends" is different from "My friends are fools" (because the first allows wise men to be my friends too, whereas the second does not); "All men are mortals" is very different from "Mortals are all men" :-)
That said, sometimes there is an equivalence, and some ideas can be expressed either way. In these cases the verb will agree with whichever you choose to make the subject ("One side-effect is headaches"; "Headaches are one side-effect").
(Note that in your examples, "**Our goal were the mountains" is wrong - in standard writing it should always be "Our goal was (complement)". But you could say "The mountains were our goal", with the same basic meaning but different emphasis.)
Addressing your second question: wholesale inversion of a "to be" sentence (where a sentence of the form "noun copula complement" changes to "complement copula noun") is rare, except for in specific situations:
- Questions (because English likes the question word to go first: "Who is Fred? Fred is the tall man"). The inversion always happens unless there's a specific reason not to (perhaps expressing surprise - "He's whose brother?")
- Certain comparative expressions ("Better still are the ones that follow"). The inversion here is optional ("The ones that follow are better still" is fine too).
- Expressions describing location. The simplest in this category are "There is...", "Here are..." and friends, but I'd also include in this category "Next to my house are two restaurants", "Found in every city are cars and buses". This inversion is optional.
- Poetic effect - either for emphasis, or for reasons of metre/rhyme ("Blessed are the meek" - the natural phrasing is "The meek are blessed"; the inversion serves to imply a very great level of blessedness; "Old King Cole was a merry old soul, and a merry old soul was he" - the inversion is clearly unnecessary but nicely fills up the line)
Note that in these situations (except possibly the last), it is usually very clear from the construction that the word or phrase at the start of the sentence is not the subject - often because it's an adjective or adverb phrase. In situations where the distinction is not so clear - such as the examples you provided - inversion will rarely if ever be used (since the sentence tends to end up sounding plain wrong, rather than inverted).
Do note that there are a large number of situations where a slightly different form of inversion ("noun verb complement" changing to "verb noun complement") is used - where it is forced or allowed by the use of certain forms or expressions. Examples such as "Is he tall?", "Never am I angry" are examples of this second kind. I won't attempt to enumerate these, because for one thing there are a lot of them, and for another I don't think the uncertainty you're concerned with arises here. In any case, here is a list of uses of inversion, that contains both types.
[Edit to respond to edit in question]
I have to agree with Fowler about the time periods: the "six months" is considered a single unit, so the singular is used; this is common when referring to measured quantities:
- Ten pounds is a small amount to pay.
- Two litres is more than enough.
We can tell that this is not inversion by using a verb where the ambiguity doesn't arise:
- Six months seems like an eternity.
- Five dollars buys me a very nice lunch.
We can construe the sentence like Fowler as meaning "A period of ...", "An amount of ...", or equivalently by considering the phrase as meaning "Six months of time", "Five pounds of money"; mentioning the uncountable noun makes the reason for the singular clearer, and distinguishes this case from the "light of the stars" case, where there's no obvious way to do the same.
(The plural can sometimes also be used in these cases, giving a sense of referring to each of the individual items mentioned "The six months are dragging on slowly" emphasises that every single one of them is felt.)
In CaGEL's terminology, it's clear as day how to figure out whether a complement is a core or non-core complement.
Ditransitive/monotransitive contrasts
i I gave her the key. I gave the key to her.
ii I envied him his freedom. I envied him for his freedom.
iii They offered us $100. They offered $100
iv They fined us $100. They fined us.
In i–ii the contrast is between a ditransitive construction containing two internal core complements, Oi + Od, and a monotransitive one containing Od + a non-core complement with the form of a PP, while in iii–iv it is between a ditransitive construction and a monotransitive containing just one internal complement (Od).
(Page 297)
Here, CaGEL says both her and the key in I gave her the key are core complements, and that both him and his freedom in I envied him his freedom are core complements, even though you can have a grammatical construction even without her or his freedom as in:
I gave the key.
I envied him.
That is, CaGEL says NP complements that can be omitted, as well as those that cannot, are core complements.
Also, see:
Core complements are generally more sharply differentiated from adjuncts than are non-core complements, and there is some uncertainty, and disagreement among grammarians, as to how much should be subsumed under the function complement.[Footnote 8]
[Footnote 8] Some restrict it to core complements, taking the presence of the preposition in, say, He alluded to her letter as sufficient to make the post-verbal element an adjunct; this makes the boundary between complement and adjunct easier to draw, but in our view it does not draw it in a satisfactory place, as will be apparent from the following discussion.
(Page 219)
Note in the footnote that CaGEL treats to her letter in He alluded to her letter as a non-core complement even though the PP cannot be omitted.
In CaGEL, therefore, whether you can omit a complement is a non-issue in determining whether it's a core or non-core complement. All PP complements are non-core complements; and all non-core complements are PPs.
Best Answer
Your analyses of (1) and (2) are both correct. They do indeed refer to the ‘as X as Y (is)’ construction.
Your analysis on (3), however, is not quite right. ‘Ever’ when used as an intensifier is confined (as far as I can think of) to three specific circumstances:
With comparatives: When used before a comparative adjective, ever intensifies the comparativeness of the adjective (not the meaning of the adjective itself) and means something like ‘increasingly’: “He had to borrow ever larger sums of money to cover his gambling debts”. [Registers: all]
With ‘so’: The phrase ‘ever so’ cannot really be split up or analysed, semantically: it just means ‘very’: “Oh, he was ever so bright as a child”. [Registers: informal, colloquial]
With interrogatives/indefinites: When used after an interrogative or indefinite pronoun/determiner (often cliticised), ‘ever’ intensifies the meaning of the interrogative/indefinite: “However are we going to do that?” – “I can see nothing whatever”. [Registers: mostly somewhat formal; not common in informal or colloquial use]
In other cases, ‘ever’ has a more literal meaning: ‘at any time’ (used in questions and negatives), or ‘at all times’ (used in positive statements, somewhat rarer than the negative/interrogative use).
This is also the case in the sentence you quote: it means ‘at any time in the past’ here, and it refers to the verb, ‘heard’. The placement of the adverb before the subject and verb is rather formal and somewhat archaic, but may still occasionally be seen even in Modern English. The verb is in the simple past tense in this example, which is also somewhat archaic—in current English, you would usually expect to see a pluperfect there. Thus, the sentence can be recast with no difference in meaning as:
The construction “(that) ever [subject] [verb]” is quite common in older literature and folk songs; for example, the traditional Scottish and Irish song The Parting Glass uses it several times (with ‘ever’ being contracted to its poetic/archaic variant ‘e’er’):
These examples also show that the simple past tense and the perfect/pluperfect are fairly interchangeable in this particular construction.