Ghost of a Chance:
After a rather nasty break up with a girl that just didn't understand him, Dr. Spengler decides that it would be nearly impossible for him to find a relationship. On a routine haunting call, the guys discover a ghost that is like Slimer (a conscious spirit), but who can actually speak and can take on a more human form (unlike Slimer's blob form). They are very surprised to see that she doesn't run from them or even resist when they put the ghost trap out. Egon and Ray think she could be of great use to the Paranormal science society. Giving them details about what it felt like to die and things of that nature.
Ray, being the more social and sympathetic of the Ghostbusters, talks with her privately about it. Asking her to come stay with them for a while and let them run tests on her. Having nothing else really to do with her eternity, she agrees.
While running tests on her, Egon and her speak quite a bit. He realizes, a bit sadly, that she's the kind of girl he's always wanted. Kind and non-judgmental, unclouded by heavy emotions, believes heavily in logic (despite the fact that she's a ghost), even loves Twinkies (which are Egon's favorite food)...or rather she used to like them. Even though she was rather emotionless as a human, her ghost form does force her into small fits every once in a while. During one of these, she confesses that she wishes she knew him when she was still alive.
***For the way her spirit is, I was figuring something like the ghosts from Harry Potter. Full forms, lacking much coloring, and being able to communicate verbally. But unlike the Harry Potter ghosts, I would like her to be able to have a sense of corporeal form. Kind of like how Slimer can hug them and touch stuff, but at the same time just pass through things if he wants to. This would allow her to touch him, but not give him much in the way of touching her. I figure the game would be more romantic than sexual.