The first conjunctive, so called, that I note in the Hebrew for Christians site is the munach ב֣. Although it joins a syllable to the next few syllables, it also separates that syllable from the prior syllable. Rather than the terms disjunctive and conjunctive, better I think is to consider that the accents below the text define the separations of the phrases of a verse. Some define these separations more substantially than others. The final note in each verse, silluq, (occasionally missing as in Numbers 25:19 as noted in the prior post), the major cadence (atnach in all books), and the secondary cadence (ole-veyored only in the three books).
All the signs below the text separate 'phrases' though the phrases may be very short, like only one word. This is because some notes are not as frequently used for recitation as others. Every sign also marks the syllable on which the current word is accented. So the accents are all great helps in pronunciation. Where there is an ornament, the syllable is typically stretched out longer to give the singer time to enjoy the emphasis.
So far I have never seen or heard a situation that departs from this simple explanation:
below the word, the accent defines a change in reciting note. All words on the same reciting note are a set of related conceptual phrases or sentences. Above the word, the accent defines an extension to the syllable. All accents indicate word accentuation.There is no need for kings, dukes, princes or otherwise and no servants that I can define that would make this clearer. It's not really an issue of grammar either. Grammar is taken for granted, not derived from accents, though I expect accents may resolve ambiguities also, perhaps especially for homonyms. My preliminary post trying to discover the meaning of conjunctive may still be helpful in sorting out the traditional names at least.
I have seen this Bible Society publication before and it is still mystifying to me. I think if I read it closely, I would find assumptions that have to be questioned. Like many prejudices, it starts out with what it wants to prove and never proves it. It contains a variant on the classic escape clause "While this system is very graphic and is a very useful teaching aid, it does not convey what actually happens in the text." (My italics).
Nonetheless, bolding my own prejudice, you could, if you were so minded, look at every one of their examples with the music and learn the way of the music and three other ways of confusing yourself (Hebrew emperor hierarchy, mathematical node theory, and punctuation).
If I put out a comparison, perhaps someone will explain it to me. The answer seems to be in the music without explanation - much the more transparent to read, I think.
Now let's see the music
Here's a possible English underlay:
And [B] God constructed the [F] two [G#] great [A] lights,
the [C] light that is great\er to [B] govern the :day and the [C] light that is less\er to [B] govern the :night, and [G#] the [E] stars. Or perhaps 'a [G#] long with the [E] stars'. Many English translations add some words which could be pearls hanging along the final triad.
Sing this - it is beautiful.
[Postscript] Deep inside me, not quite articulated, is the possibility that the ornaments could imply a slight pause like a comma after each one... Here the : (zaqef) separates subject and object, and the \ (pashta) the subject of the infinitive from the infinitive. Perhaps this is common but I would not dare to say at the moment. Children don't learn grammar or expressiveness of language in this way.