I believe tritypes have been used in the opposite way that they should have been. Tritypes have been used to simply design quick categories, rather than to describe the complicated chains in which our emotions and our stories are written. I believe tritypes work as self-reinforcing scripts with core importance placed on the middle enneagram and the first and third as the supporting views. I also believe there are certain rules and criteria's that can give order in the chaos that sometimes has come to define Enneagram theory. This will make tritype theory more valuable and beneficial.
Your Dominant Type
My best fit tritype has been the 9-5-2. This is often referred to as "The Problem Solver" archetype. If I select the Enneagram that I believe has come to define me the most it is the 9. This enneagram is more common in people that have experienced conflict and disharmony growing up. Because of this lack of harmony growing up, we place a core importance on acquiring and maintaining harmony around us.
Another good way to identify your core secondary value is to find which value has been implicitly discarded. The 8, 9, and 1 Enneagram types have discarded their instinctual tendency. This means they will ignore or discredit their need to feel safe or at peace in order to focus on their gut and what they want or desire, their drive for self-preservation, love, or belonging is of low importance. They will rather work to become better, to gain more power, or to maintain peace around them.
The dominant type should be placed in the middle and the other two should be understood as secondary drives. The 5 and 2 here serve to build up and direct my Enneagram 9 drive. So how does that work?
The secondary drives are best understood as compensating in their role. A 9 wants balance and harmony. The head (5 in this case) serves the role of explaining how to maintain balance and peace. Enneagram Five will describe that disharmony is a result of weakness or inability. Because you lack understanding, or are not good enough, or don't work hard enough, you cause conflict and struggle around you. This can be compared with the 972 tritypes that feel pressure to be fun and enthusiastic and hopeful at all times to keep others from arguing or fighting amongst one another, or the 96x that will always feel a need to check up on everyone to make sure nothing is wrong. "Did I offend you then...?"
As the heart types (234) are all about how we feel as people and how we see ourselves, 2s tend to want to feel a degree of pride over what they do.
They want to make sure that they can rationalise and explain to themselves that they have made good choices. "I did it for everyone, for my family, or for the greater good." the two will say. The 9-2-x will believe disharmony is a consequence of being a bad person and that people argue with you because they dislike you.
The 9-3-x will believe conflict is a result of people not listening to you or taking your advice. The 9-4-x will believe conflict is because of something that is wrong with you as a person. That there is something about you that people just don't like. This can fuel some 9s to take on an outcast status (9-4-x) where other 9s will take on a martyr or scapegoat status (9-2-x).
The High Vs The Low
It's important to look at your highs as compared to your lows. When you experience highs, you look at your enneagram in a positive manner, and when in a low, you look at it more negatively. The 9-2-5 high will make you feel that you have harmony, and that it is because you're a good person, and because of your unique skills and talents as a problem solver.
The 9-2-5 low is a feeling of having caused conflict and disharmony, as a result of being a bad person, who lacks the necessary skills and abilities that can be of use to help other people. (I can't find solutions, I don't know what to do, I'm a terrible person, this is why people are upset.) It's important to note that none of these views are objectively correct or incorrect. It's just a reflection of your emotions as the orchestra and you as the director.
The Lost Type
I believe the three instincts (Sx/So/Sp) serve an integral role in the Enneagram and should be looked at together with your enneagram type. They should rightfully be placed as an opposing drive to the gut, just as the head types (567) tend to have somewhat oppositional roles to the heart types (234) the gut (891) serves an oppositional role to the instincts (Sp/Sx/So). The lost type is the number or quadrant that is not in the mix. This represents neglected needs in us. This is important to acknowledge. Everyone has a hidden fourth type that represents things they don't dare to admit to.
Perhaps the 9 has a deep, hidden need to fit in (So), or a need to be loved (Sx), or a need to just survive? (Sp) that is hidden in the mix? This one can be hard to spot because we rarely talk about it or admit to such feelings.
The importance of the big picture
Tritypes can be important because they show us the bigger picture. There may be positive beliefs in our enneagram that reinforce bad behaviours. See "The road to hell is paved with good intentions" There can also be negative drives that serve to fuel positive behaviours.
We rarely just feel one emotion - usually humans are more complicated than that. We have anger, and we also have shame, and perhaps also anxiety in the mix. Emotions tend to mix and dance together and thoughts and values do the same.
We all fall into these spirals of behaviours. The 9-2-5 spiral is a spiral of working excessively to think of solutions to solve conflicts and to help other people, of feeling guilty for conflicts and disharmony in the world, and wanting to make things better. But it can also be a spiral of good deeds, solving conflicts, finding balance, and helping to solve conflicts and struggles in the world. If it is unhealthy or healthy depends on your level of emotional stability and neuroticism.
Neuroticism as the final factor
To know if something is healthy for you or not, know how it feels in you and what emotions it forces up in you. If you don't like the story you're telling or how you respond to it, find another. And ofcourse, never overdramatise your own ability to make a situation better, and don't blame yourself unnecessarily for a chaotic or difficult situation. The world is far too complicated to blame on any individual person. We're all better of working together.