I've got one, I don't find her any more neurotic than my wee tabby - definitely needy though, lol
She doesn't disappear doing cat things, she's like there , if you tidy something out, she has to come and see what you're doing, preferably between you and whatever you're doing, if you're on the computer she wants to come and see what you're doing, preferably between you and the keyboard, if you read a book she comes and stares at it, sitting between you and the book... I'm sure you're getting the picture about that, lol.
She'll randomly decide that she needs to be on your shoulder while you do something and if you don't respond to her asking politely (otherwise known as yowling at you) she'll just jump up there, because that's clearly where she thinks she should be, if you sit down - even for a couple of seconds she's looking for a lap to cuddle in to. If you're not doing something, she's not overly demanding, she just likes to sit with you.
She plays a lot, not by herself or with the other cat though - she brings you toys so that you can throw them and she can fetch them back. She also quite likes it if you turn her on to her back and hold her like a baby in your arms 
She randomly has chatty moods, where she'll meow at you for no reason, it does quite amuse visiting children because you can tell her to say meow and she does.
She's fairly laid back though, strange people are good, she'll go and demand the stroking that she clearly feels is her due, she's quite happy for children to maul her a bit, it doesn't freak her out if you move furniture or change routines, she's currently on regular medication and I shake her pill bottle and she comes and jumps on my knee to be given her tablets.
She doesn't go out much, her coat's quite thin and she really feels the cold, so there's no option of getting rid of the litter tray, she also doesn't see why you should get to go out without her, so she'll greet you at the door complaining quite loudly if you've been out for a while, but she's quite easily mollified by a bit of apologetic stroking.
I don't know if all of that is typical Siamese behaviour, but a lot of it is - I think you either adore them or they completely do your head in, lol. You're very actively loved with a Siamese, my other cat, I get the impression that she's quite fond of us, but really it's about the food, I know the Siamese loves me, lol, and it is me, she's picked me as her person out of all of us.