I am going to take a shot at answering this question, please feel free to correct me. The verb has to match the subject.so wants is correct. I believe.
He- Subject Noun
wants - verb transitive
to go - direct object (infinitive functioning as a noun, in the role of DO)
on vacation - adverbial phrase (prepositional phrase functioning as an adverb in the sentence answering the question "wants to go where?") (on- preposition, vacation- object of the preposition)