I don't know. I think it is best to consider "right about now" as a phrase, that has a meaning as a phrase, and can't be analyzed grammatically. You can't deduce the meaning of the phrase from the individual words and the grammar. If forced to think about it, I would say that it is a preposition, and that it carries the idea of a vague or indefinite time. For example, right now where I am sitting it is 5 p.m. on March 16th. "I'd like to be in Hawaii right now" means "I'd like to be in Hawaii at 5 p.m. on March 16th." Maybe I want to be in time for something that will happen later this evening. "I'd like to be in Hawaii right about now" means "I'd like to be in Hawaii at about this time of year, more or less." Or, "I'm feeling kind of tired and bored, and whenever I'm feeling tired and bored I'd like to be in Hawaii."

In this context : about = approximately = more or less. It can be considered both as an adverb and a preposition in this context. Probably more like an adverb .

By function, are you asking for a specific grammatical name? If so, I am not sure. Otherwise, the "about" in that sentence is dealing with when (time) you would want to be in Hawaii. It is saying that "now" would be a nice time to be there. Hope that helps!