***** NOT A TEACHER *****
I have done some research and am delighted to share some ideas (not "answers").
1. It's easier to parse a sentence if one simplifies it. So let's parse "I wanted to look nice."
2. As I understand it, you want to know what the verb phrase is.
a. I wanted to look nice. (The infinitive phrase "to look nice" is the direct object of "wanted.")
b. I wanted to look nice. (The adjective "nice" is the subjective complement of "I.")
3. In my OPINION, the "correct" analysis is 2.a.
4. You used the term "intensive verb." I had never heard that term before. I then realized that you were probably referring to something that many books call the complementary infinitive. That is, a verb + infinitive are closely related, so they form the verb phrase.
a. A good example is: I have to eat dinner now. "Have to eat" is the verb phrase. It = I must eat dinner now.
5. In my OPINION, "want to look" does NOT meet the qualifications to be a complementary infinitive (or, as you say, an intensive verb).
6. Therefore, it seems that we can parse your sentence like this:
I = subject.
wanted = verb phrase.
to look nice. = infinitive phrase that is the direct object of the verb.
As you know, in such a sentence, the subject of the infinitive phrase is the SAME as the subject of the main clause.
Native speakers will NOT accept: "I wanted I look nice."
But they WILL accept: "I wanted TO look nice." ( Some books claim that the function of the "to" is to remind us that the subject of the infinitive is the SAME as the subject of the main verb.)
Main source: Randolph Quirk and three other scholars in their A Comprehensive Grammar of the English Language. I have the 1985 edition. See page 1187.
Student or Learner