Noetisexual — It’s a mental attraction rather than a purely "intellectual" one. It’s loving the shape of their mental landscape and wanting to explore it. It’s falling in love with the way they think, their unique mental make up. It’s loving their creativity, their ingenuity, their silliness, their humor, their emotional intelligence, the way they use words, or the way they make mental space for you in their minds, and more.
It’s being attracted to the way their minds work — not how their brain functions — rather than simply one ill-defined facet of it. Noeti can serve as a prefix in itself: noetisexual, noetiromantic, noetisensual, etc. Noetilinking,the general experience, is not a sexuality per se; it can be a type of attraction like sensual or emotional are types.