If the person leaves the room, or otherwise obscures themselves from your view, the last ability will stop having any effect. If they return to your view, the last ability will function once again. They don't even need to know that they've been chosen; you can tell them if you'd like, but they may take that as a sign to get up and go for a walk.

You don't have to be always looking at the person in order for the last ability to function. It just needs to be possible for you to see them from your seat. This isn't a gotcha game where your opponent waits for you to blink and then quickly activates abilities.

If the person leaves the room, you can't pick up your seat and follow them. Your seat stays with the game with you in it.