How do you get the scooter on night watch island?

You use it at the start of the island, to get the job.

When the crook steals a security cart, Gus suggests that you get the scooter in the Mall office. The code word is FROST. Go to MacGuffin's to get the quick charge device for it. When you leave the office, go to the west wing, then return to start the cart chase. Go to the top of the escalator (left side) in the atrium and the cart should drive by (it's actually a dummy driver). This sequence can be difficult to start for some reason, as the cart is driving places it cannot go.