Whoever told you that was oversimplifying a bit. (And the idea that statives can't be used with progressive tenses is also oversimplified, as I stated in an answer there.)
It's true that in this sort of case, "just" is almost certainly used to mean "only" instead of "recently". But stative verbs in English simply aren't that hard-and-fast a category, so there's a bit of wiggle room that could allow someone to use "just" in an unusual way for wordplay. This is especially true because the idiomatic way to mean "only" is
"I just wanted to ask a question."
I think this is because "just", in the sense of "very recently", makes less sense to use with something in the more distant past, which tends to make it more obvious that "only" is the correct meaning.
But using present perfect instead of past tense implies that there's some present relevance: that maybe you still do want to ask the question. And that brings back up the possibility of meaning "very recently".
There is an unambiguous way to refer to the recent past using "just", though:
"I just now wanted to ask a question."
(At a time in the very immediate past, I had a particular desire, and probably still do.)
"I just started wanting to ask a question."
(Beginning in the very immediate past and continuing, I have had a particular desire.)
You should avoid using an unusual and ambiguous construction like "I have just wanted…" unless you have a very good reason. Either of the two possible meanings can be phrased more clearly.
Best Answer
Become is a contraction of come to be, which is a general Inchoative (change of state) predicate,
like start, finish, end, begin, and continue.
Inchoatives change states, but change between states may be gradual, allowing for optional continuous constructions, under the right circumstances. These all mean the same thing, for instance: