That's the back side of the center console. A few of the announcement videos from the LA Auto Show have pointed it out. I believe it will be on all Priuses. The promotional images from Toyota's US newsroom show the switch on the dashes of both the Prius(Limited) and the Prime(XSE Premium), and the inverter is not listed on the option sheet for the different trim levels. That suggests it's standard on all trims.
Gen 3 has a 125 amp fuse, rather inconveniently buried inside the under-hood fuse box, between the DC/DC converter and the cable back to the battery. There is a 140 amp fuse in the + battery clamp end of that same cable. If an inverter connection is made (as I've suggested in the past) on the cable side of that battery-clamp fuse, then the added connection is protected both from the converter (by the 125 amp fuse) and from the battery (by the 140 amp fuse). Also, it is then only one fuse drop away from the converter, whereas it would be two if connected right at the battery + post. In Gen 2, the fuse at the front end of the cable is 100 amps (it's part of the long white multi-fuse-link), and the one at the battery clamp is 120 amps. The principles are the same.
Prius' 12v batteries, like all car batteries, have a limited lifespan. They can last for five to six years, if not longer. However, if you don't use them for an extended period of time, they weaken, and if you don't drive your Prius on a regular basis, they deteriorate and die.
In this case it hasn't got much incentive to, as the far end of that hose is hanging open to atmospheric pressure. You could maybe count the molecules that are going to permeate through the rubber hose instead of going right where it's easy to go, but you're not likely to notice breathing them or igniting them.
