The second section of the verses resonates with me as being evocative of early '70s songwriter pop: Gilbert O'Sullivan and I'm not sure what else. With Klaatu, though, these are only sections in a progressive-minded compositional context, occurring after the excellent, Beatle-esque first parts of the verses.
The chorus also seems to me to be of the same genre, but it only occurs once in the song! And it carries itself perfectly to its conclusion.
In the third and final verse (hastening the song to its structurally appealing end), John Woloschuck's lyrics take that same second part of the verse and invest it with enough drama and enough poetry that the effect is completely transcendent:
I stand here in the queue behind a foul cigar
My face discreetly buried in a book on Mars
And I'm waiting on the pier 'til Charon comes
Entire Klaatu catalog on BullseyeSongs.com