One might think that to pursue (desire, hope for) something is to pursue it either as a means or as a final end. But that is false. Here is a nice case. Let us say that you don't know whether symmetry is worth having for its own sake. An omniscient being (or just an axiological expert) tells you that you will be better off for ensuring the existence of large symmetrical patterns on your walls. You ask whether this will be good in and of itself for you, or whether it is merely instrumentally good. The being declines to answer. You now have good reason to pursue the large symmetrical patterns on your walls (and desire and hope for them). But notice that you are not pursuing the patters as either a means or as an end. You are not pursuing the patterns as a means, because you do not believe that they are a means to anything valuable. You are not pursuing them as a final end, because you do not believe that they are intrinsically valuable. Instead, you believe the disjunction of the two value claims, and that is enough to justify your pursuit (and desire and hope).
In fact, this sort of thing is quite common. We have good reason to think that something is valuable, say because friends we respect pursue it, but we sometimes don't know whether it is valuable merely as a means or as an end. But this ignorance doesn't stop us from pursuing it. Thus, one may well pursue good reputation without having settled whether it is intrinsically or instrumentally worth having.
It is common to divide up pursuit (desire, hope) into the instrumental and non-instrumental. If so, then this case counts as non-instrumental, simply because it is not, in fact, instrumental. However, the term "non-instrumental" is often used as if it were more than just the denial of "instrumental". A "non-instrumental desire" is thought of as a desire for the thing itself, for instance. The above shows that this is mistaken, because it makes one think that there is a dichotomy where in fact there is a trichotomy: the instrumental, the intrinsic, and that which is neither instrumental nor intrinsic.
I've for a while been bothered by the phrase "non-instrumental value", which makes it sound like it's a derivative notion with the basic notion being that of instrumental value. And now I see that I have good reason to avoid the phrase. For non-instrumental value corresponds to non-instrumental pursuit. And the category of non-instrumental pursuit is not a natural way to slice things up: it is a disjunction of final pursuit and neither-final-nor-instrumental pursuit.
Interestingly, though, while the phrase "non-instrumental desire" is extensionally problematic given the kinds of cases I've been talking about, "non-instrumental goods" does manage to be extensionally right: it slices axiological nature along its joints, because the third category that arises for pursuit, desire and hope arises from subjective considerations, and hence does not apply to the good itself. But, nonetheless, it is better to avoid the phrase. "Intrinsic" or "basic" is better.