"Unmanifest" refers to something that doesn't exist. It begs the question, "Are there multiple types of existence, or is existence an absolutely abstract category, admitting only one of two possible values?
"Non-existent" and "unmanifest" are useful adjectives, given the grammar of our language. A writer might say, "The General found supplies non-existent." That doesn't mean he actually found supplies (objects) that were non-existent. It does mean that he came to understand there were no supplies. "Non-existent supplies" is a formulation that describes a situation. "Non-existent" isn't meant to describe "supplies" (unless the intent is humor.)
"Unmanifest" can be used to describe qualities that are absent. "The General's courage is as of yet unmanifest." Courage is a quality that a person may, or may not, manifest. Here "unmanifest courage" describes an evaluation of the General, but "unmanifest" is not really an adjective describing his "courage". "Manifest" and "Unmanifest" describe things that don't have physical existence, or the nature of whose physicality is ephemeral (eg. a smile or a thought).
A thought is a particularly good example of physical and non-physical reality interacting. We sometimes consider a thought as an abstract reality, that doesn't require a living person to be thinking. Thoughts can reside in books, grammatically, at least. And since thoughts can be expressed in so many various ways, it seems that they are not dependent on any particular physical objects. And yet our own, current thoughts have quite a tangible reality to us. If it is not actually our thought that is tangible to us, then at least the sensory experience that gives rise to it is. But I feel that I experience my thoughts as much as I experience light, sound, heat or cold. So is a thought an abstract or a tangible thing? Or both? Is my thought an expression (or manifestation) of an abstract thought? I want to say yes to the latter, but it leads me to the idea that something can be unmanifest, and yet exist.
Existence has a strong implication of physical reality in my thinking. I don't want to BE a thing that exists only in logic or imagination. I want to BE a physical body. Existence, other than physical existence, is fine for prime numbers between 1 and 10, but I don't find it appealing. To much like not being alive, which is too much like being dead. So, I want for "existence" to really mean "physical existence". I don't want to be unmanifest, because is seems too much like not being around at all.
But if you have a strict definition of existence - that it can only on or off, true or false - then an individual person's existence is on shaky ground. The working definitions we use to define ourselves fail at the boundaries. Are you your will? Your sensory experience? Your body? Some combination of these?
The thing most present and tangible in your existence is also the thing least definable. And the thing you cannot ever experience as an object, is also the experience itself. It is only an abstract idea, and yet it is all you have ever known. I still don't feel like I have myself figured out.