That sounds really interesting. I don't really have any ideas of what they'd come up with. She's out in the sun so she can't be a vampire. Maybe a fairy, but I don't know if the sword fits. Oh maybe they'd avoid anything supernatural?

I suspect that Elizabeth is part of the majority of Immortals that doesn't know about Watchers. So Peter and Neal could notice a suspicious person who seems to be stalking her. Cue arguments about how what they is doing is completely different from what this other person is doing. :)