You can't stay inside security. There isn't really a secure area.... when the inbound flight lands, they start processing the few passengers through the single checkpoint. They've got a cubicle wall with a couple of hard benches up next to the window that you have to walk behind the security equipment to get to. Other than that, even if you sat in there, I'm sure they'd make you get rescreened as the whole area is basically unattended except when they are getting ready to board a flight.