Neptune's Links
Neptune thinks that Elaine is very cute. He spends time with Elaine because they both happen to be friends with Sirius, but he's never brought up the idea of talking to Elaine himself. He hopes that he can overcome that nervousness and talk to Elaine at some point in time.
Elaine is very fascinated by Neptune, mainly because he is half-homelander. That means he's part dragon, which Elaine is very much interested in. He has once tried to talk to Neptune, but the latter shied away. This has made Elaine very determined to one day get Neptune to talk with him.