This topic may have been discussed here a lot, but I just wanted to be clear on it. Basically both [1] and [2] express the idea of "I" have been --- continuously --- desirous of getting the license. However, what, if subtle, difference would you feel between them? To me [2] is more vivid. I feel more about the speaker studying more for the written exam. Or, he may not have been studying yet, but must have dreamt of getting it.

[1] I have wanted to get the permit to operate the huge boat.

[2] I have been wanting to get the permit to operate the huge boat.


Sendai, Japan
The real mystery to me is that a non-progressive verb like want can be used in any progressive tense at all. And yet, there it is, as idiomatic as can be. I have been wanting ... (for weeks / months / years ). The second sentence is more common than the first. Both, but especially the first, seem to beg for a for + TIME phrase to complete the idea. The second sentence suggests that the desire for the permit has been more frequently and more obsessively on the speaker's mind.

Present progessive focuses on temproary situation and present perfect focus on long situations.

I think

Your first sentence could be that you want the permit for a long time.

You second sentence could be that you want the permit recenty.
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 CalifJim's reply was promoted to an answer.
"I have wanted" without a for + time phrase could only mean "I" just once felt the desire. And I agree with you CJ that the second suggests the desire was more repeatedly felt, perhaps one after another.