I think that intellectual intimacy should include having similar mental capacities. People tend to enjoy having others around them that are of similar capability (maybe not in the same exact way; i.e., one has stronger short-term memory retention and another in integration, but generally capable of similar levels of awareness and analysis) rather than obvious differences.
It seems that you also describe emotional intimacy and vulnerability in a coordinated way. One cannot reveal their emotions to another without having a level of trust intimacy, as you mentioned as a form of emotional disclosure.
Could it possible that these forms of intimacy are subset to trust intimacy? It seems possible that vulnerability is the core value, and these different forms of intimacy are expressions of such value. It is interesting that you mention trust-intimacy and understanding-intimacy. A part of me wants to argue that these are intertwined; a part of trust-intimacy is to empathize and understand the other's position, state or behaviors, and an inverse relationship is seen as you described as well.
I think that intellectual intimacy should include having similar mental capacities.
Seems right, for both reasons of understanding and trust.
A part of me wants to argue that these are intertwined
I think the default is they're intertwined but the interesting thing is they can come apart: for example, you develop feelings of connection and intimacy through shared experience, falsely assume you can trust (or shared values or whatever), but then it turns out the experiences shared never actually filtered for that.
John Wentworth recently posted a discussion-inducing piece about how the willingness to be vulnerable is core to romantic relationships. This is not obvious to me as the core thing. I think romantic (and other) relationships are arguably about intimacy[1]. Perhaps intimacy always requires vulnerability? To answer that, and because it's generally interesting, here is a babble[2] of the kinds of intimacy:
People often experience a kind of intimacy from sharing the same hobbies or fandom which I think has elements of both values intimacy and experience intimacy (we like the same thing and have shared experiences of doing it).
I'm struck that arguably many of these forms of intimacy are just variations on experiential intimacy: having the same experiences as another, or by extension the same knowledge as others. Sex is an experiential activity you do with another person, but so is sharing ideas or your emotions. Someone who shares your values and beliefs likely experiences the world in similar ways.
A possible underappreciated challenge for significant age-gap relationships is that life experience can be pretty different. The older person might have experienced a range of experiences the younger person is yet to, but also experiences both went through (e.g. childhood could be quite different, for example if one person had the internet and smartphones growing up and the other didn't). Of course there are many other ways for life experience to have diverged a lot, e.g. having grown up with very different socioeconomic circumstances.
Though I've mostly focused on romantic intimacy, it's illustrative to think about the intimacy people feel with family members, e.g. siblings. The connection is unique and exclusive (fixed) in that arbitrary people cannot become blood siblings even if people like to speak of siblinghood symbolically. Culturally, we implicitly assume commitment to family members. Then any siblings you were raised with will have tremendous shared experience: where and when you grew up, education, values you were inculcated with, having the same parents.
Maybe we can divide intimacy into trust-intimacy and understanding-intimacy. Commitment, investment, and vulnerability are the former. Emotional, intellectual, and other forms of experiential are the latter. Values plays into both. Trust-intimacy is very helpful in building understanding-intimacy, because giving you knowledge of myself often means giving you greater ability to hurt.
That said, I think it's likely possible to build a lot of intimacy without doing the kind of vulnerability that John points at from Truth or Dare. I think fighting on the frontlines will do. I think having intense sex will do it. And many other things that are having shared experiences or discovering past common experiences, values, beliefs, language. And yet, I could also see the case that those alone would never be enough for the basis of a really solid long-term intimate romantic relationship.
I reckon many people (perhaps myself too) have catastrophically failed to realize that intimacy of one kind doesn't necessarily imply other kinds of intimacy. I think this should be kept in mind because I think commonly we connect with new people over one or two forms of intimacy, and then can falsely assume that those imply other kinds of intimacy will exist.
And while I think it's possible to have a relationship with all the kinds of intimacy, my guess is it's rare to be maxed out on all of them at all times and you'll often want to compromise somewhere, perhaps factoring intimacy desires across different relationships, perhaps merely prioritizing.
Lastly, I think it's funny how contextual and relative intimacy and connection are. The Andromedan bar bonding of missed gravity is fictional, but there are plenty of non-fictional instances where what in one context is insufficient commonality for connection is enough basis in another, e.g. expat communities. Maybe just as personality arises from a negotiation between the individual's traits and society, the intimacy felt between two people is a function of their individual traits but also the context they're in. The impact of dating apps on courtship could be seen from this angle – the ability to feel intimacy is eroded because the context is so much different from one's previous smaller network and environ.
I'm rambling here and don't have a particularly punchy point to end on. Of course "sixteen" title is meant playfully. Interesting to break it down though.
The close synonym I could also use here is "connection".
Aiming to be comprehensive rather than factor intimacy into non-overlapping independent components.
The degree of intimacy of sex is affected by the presence of absence of other elements on this list, e.g. it is more intimate if if it is exclusive, it is more intimate if it involves non-standard acts that are a rare common interest of the participants, it gains an element of intimacy if there's vulnerability (risk) via the risk that either party might defect and disclose the encounter when this would have undesired consequences.
I'm fond of the definition of vulnerability that you've been vulnerable when you've shared something such that if the other person were to laugh, it would hurt you. Crucially, vulnerability is not as simple as sharing relatively personal facts.