Here’s my translation attempt. I honestly can’t believe I finally decided to do this, but here we go.
For once, I’ll be making allowances so the translation will sound more natural, even if some literal meaning is lost. I’ve also been forced to change some grammatical features (e.g. swapping passive and active voices) in order to maintain a similar word order and style:
[Preliminary note: the more I read, the more irritated I get by the use of 主格 in this article, and the more certain I am that the author was just using the wrong term. As such, I will be assuming that – based on context – the author intended to use 主語 in most cases, which I will translate as ‘(grammatical) subject’. If ‘nominative case’ fits better at any point, I’ll go back to that, but for the most part, ‘subject’ seems more accurate.]
Using「は」and「が」Appropriately
The things that have been constructed as explanations of means of using the particles「は」and「が」appropriately have been classified into five categories and summarised by Noda Hisashi.
（1）The method of discerning appropriate usage based on whether the information is new or old
In conversation and from context, the standard is that if the noun in the nominative case is unknown (= new information), one expresses that using「が」; if it is known (= old information), one expresses it using「は」.
・鈴木さんは校長です。Suzuki-san is the principal.（Because Suzuki-san is ‘known’, one expresses that by attaching「 は」.）
・鈴木さんが校長です。Suzuki-san is the principal.（Because who the principal is ‘unknown’, one expresses that by attaching「が」to「鈴木さん」.）
[Note: I may have over-interpreted some sentences in this first section in order to preserve the sense of 表す, but the truth is that I don’t think there’s any one specific thing – indicated by ‘that’ or ‘it’ in my translation – to be expressed. Rather, the idea is that one should speak/express one’s thoughts using the appropriate particle in each case.]
（2）The method of discerning appropriate usage based on whether the sentence is phenomenological or evaluative
A sentence that describes a phenomenon as is, without adding the speaker’s subjective assessment, is called a ‘phenomenological sentence’, and「が」is attached to the subject. In contrast to this, a sentence in which the speaker adds subjective assessments to a phenomenon and describes it is called an ‘evaluative sentence’, and「は」is attached to the subject. This is a method of discerning appropriate usage on the basis of the above.
・（looking at a dog before one’s eyes）犬が寝そべっている。The dog is sleeping flopped down on its belly.（phenomenological sentence）
・（pointing at an umbrella that seems to have been taken by someone else by mistake）それは私の傘です。That is my umbrella.（evaluative sentence）
（3）The method of discerning appropriate usage based on the point up to which the subject is relevant – up to the end of the sentence, or only within a single phrase
When the subject is relevant up to the end of the sentence, one uses「は」; when it is only relevant within a single phrase, one uses「が」. This method works on that basis.
・父が晩酌をするとき、つきあう。I keep my father company when he drinks during dinner.
・父は晩酌をするとき、冷や奴を食べる。When my father drinks during dinner, he eats chilled tofu.
（4）The method of discerning appropriate usage based on whether or not the nominative case expresses a contrastive meaning or an exclusive meaning
If the nominative case has, relative to some noun of the same type that does not appear in the sentence, a comparative meaning similar to ‘by comparison, it is […]’, then「は」is used（contrastive「は」）; when it has an exclusive meaning similar to ‘only this is […]’, then「が」is used（exclusive「が」／「が」of generalisation）. Discerning of appropriate usage is performed on this basis.
・犬は好きだが、猫は嫌いだ。While I like dogs, I dislike cats.（expresses a contrastive meaning）
・ 私が責任者だ。I am the person in charge.（expresses that among those present here, it is not someone else, but ‘I’ who is the person in charge）
（5）The method of discerning appropriate usage based on whether the sentence designates something (指定文) or formulates a proposition (措定文)
The predicate of「貴乃花は横綱だ」=‘Takanohana is the yokozuna’ expresses the nature of the noun that acts as the subject, and the sentence cannot be reformulated as「横綱が貴乃花だ」. Such sentences are called「措定文」, and「は」is used in such sentences. In contrast,「鈴木さんはあの人だ」=‘Suzuki-san is that person’ expresses that the noun in the predicate and the noun that acts as the subject are the same thing, and it is possible to reformulate is as「あの人が鈴木さんだ」. Such sentences are called「指定文」or「同定文」(‘statements of identification’), and in such sentences,「は」and「が」can both be used.
・地球は、太陽系の惑星だ。The Earth is a planet of the solar system.（措定文）
・あの人の趣味は、勉強だ。That person’s hobby is studying.（指定文）
Sorry about the late reply. I was a little busy, as you can see. 
Thanks for all the effort you put into explaining how Rubin goes about things and for providing that link. I took a quick look, and while I probably won’t buy the book, I see what you mean about not just sticking to tired explanations and making an attempt to adapt things to what readers are likely to be familiar with.
This is something I heard a long time ago, actually, but yeah, maybe it’s not such a common thing in textbooks. The first resources I used when I was just dabbling in Japanese (and not formally studying it) were books that seemed to target specific parts of Japanese grammar and websites, after all.
I wouldn’t be so sure, if only because I think one still notices a difference upon hearing the copula. However, yes, perhaps it isn’t necessary to meaning and only provides extra confirmation or an additional nuance that doesn’t strictly speaking fall under a copula’s functions.
Or we could say that it relates to what is standard or well accepted.
What I thought about that^ was effectively this:
But see
I’m a prescriptivist. The reason being that I believe that standards are needed, if only for the purposes of teaching and communicating with as wide as audience as possible. I don’t think that any sort of usage should be imposed on a population, but the fact is, primarily due to various social phenomena, at least one of the possibilities is going to given a place of honour as the ‘standard’, and people who fail to be at least capable of using that standard when such usage is expected are doomed to be shunned by the most prestigious circles of society, or to at the very least be completely misunderstood.
The reason I can’t embrace descriptivism wholeheartedly is that if I had been a descriptivist, none of you would be able to understand a single one of my sentences right now. Wha’ u wld see ah, wld be liddis. No standud gramma, esp if I spell duh way I pronouns n yous SMS language. Laki I dun use Hokkien, oderwise y’all liak bo kyou. That or I would appear intellectually challenged. I’m from a country where there’s supposed to be a standard, but very few people are capable of imitating it with any respectable level of consistency, and the end result is that people who visit us tend to have trouble understanding us, and it’s pretty clear that some people think we speak English very poorly even though, ironically, a good number of people write very proficiently in English. If we used ‘enough people use it’ as the standard, Singlish would be a completely different dialect by now, no one would speak standard English, and no tourist would be capable of communicating with anyone in Singapore. A bare minimum of prescriptivism is necessary, especially in a globalised world where people have to be able to stand on the world stage and receive a modicum of respect when communicating their ideas. I would quite happily leave usage to its business otherwise. And that is also why in every language I learn, I have two boxes in my head: one for perfectly standard usage, and one for all other contemporary usage I need to know in order to fit in socially.