I've been analyzing these connections between the systems for probably 20 years looking for commonalities and differences. In answer to your question, I have never researched the original four temperaments. My lens has been towards Kiersey temperaments but yes, I believe many of them do tie back to all of the same things. Here are examples:
The first book I read about personality type was something called The
Platinum Rule, which included four types: Director, Socializer, Thinker, Relator. Interestingly, they had 16 types, where you would have a primary and secondary of any of those four (sound familiar)? I came out as Relating Director but close between Relating and Thinking (think Enneagram 6 for relating + INTJ for director).
Then I read about MBTI, Kiersey and Cognitive Functions. We all know what those types are. It seems to operate from three perspectives -
1) The dumbed down polarities version (P vs J or N vs S) which was created to simplify things for an uneducated public; later enhanced to include the facets under each letter, making it more interesting but somewhat distorting the original concept which had been based on jungian functions
2) The more nuanced ordering of the the first two of the 8 cognitive functions, which I think is the more logically consistent way to view things and I thought what MBTI was supposed to be based on anyway
3) Kiersey Temperaments, which seems like a creative interpretation of the first two, adding it's own spin, but fundamentally sound in some really important ways. I tend to think of parts of it as genius and other parts fiction
On those three, I tend to lump them all together with a view that #2 is the actual correct way to look at things, with 1 and 3 offering useful shorthand that is imperfect in real application.
There is
Helen Fisher's system which she uses for Match.com. Her types which roughly correspond to temperaments are Builder (SJ), Explorer (SP), Negotiator (NF), Director (NT). Of course, she has a similar thing to the Platinum Rule, where there is a primary and secondary dimension - again totaling to 16 types. I have tested as a Director primary and Builder secondarily. She has another system for businesses to use, which includes Driver, Guardian, Pioneer, Integrator. I'm not sure if it's the same exactly as the dating thing but on that, I came out as Driver primary and Pioneer secondary, which is pretty much an INTJ profile. The key difference in her research is that she focused on the hormones in our bodies or something and not specifically on cognitive thought processes. I have wondered if there is some kind of relationship between those two that nobody has researched or published on.
There are more. I read a book called
Brainstyles, which had four key types are deliberators, knowers, conceptors, and conciliators. Conceptors are sort of like NTs but not completely. Conciliators are sort of like NFs and Deliberators like SJs - but the match wasn't perfect. There is another book that was once popular called
The Art of Thinking.
Sally Hogshead's stuff is more recent and interesting but I don't know quite what to make of it yet. It seems like further derivation and nuanced version of MBTI. I could bore you with others, but that is a summary of a few of the major ones I've looked at, which all seem to derive from a temperaments and cognitive brain function/thinking patterns.
Enneagram to me is a completely separate and different system and one that provides completely separate data points. I see it as based on basic fears and distortions in the way we perceive and respond to stimuli. A INTJ 5 vs 8 vs 1 vs 6 for example is going to have some substantial differences, and I do believe that each of the 16 types has a wide variety of possibilities for enneagram, though there are
obvious commonalities. Instincts are really important as well and have nothing to do with temperaments.