I take Doris around on my shoulder a lot, but she doesn't usually stay there. She will usually wander around to the back of my neck, climb down the front of my shirt, and basically do whatever she feels like doing. She has excellent balance and I'm very careful, and we can usually work something out for both of us.
What i do with my gusy whjo decide to move around at a time when they shouldn't be. If they start to walk down your chest lean forward slowly and sometimes they will shuffelback onto your shoulder and you can do teh same if they try to go down your back or down the sides etc. I've noticed my boyz will go back to my shoulder and sometimes the girls just keep going. So more or so it will depend on the rat. Oh and something that has helped me is if they start to go down your arm don't lift it or else they can learn that you'll do that everytime they want down. Something to try if you wish.
Like everyone said, some rats will hang out on your should and some won't.
My dude rats were a lot more calm back when I had them and they would usually hang out, but my recent female rats except one won't hold still long enough to hang out on my shoulder. Sometimes I worry they're going to fall right off, they're moving so much.
Like everyone else has said, it really depends on your rat's personality. Siam is my 'best' shoulder rider at the moment, but my best of all time was my 1.5lber Lestat, who would sleep in my hood for hours if allowed.
i couldn't resist sharing some hilarious pictures of my wrinkly rat chillaxin in my hood too. she used to do it a lot more when she wasn't such a pooper. now all she wants to sit on is my keyboard which makes me nervous because sometimes she's a piddler...