Not saying that just because the airlines I flew for did it a certain way, it's right ... but surely there is a Closed Loop thing here ?
PF: "Autopilot 2"
PNF: "Engaged"
To me its not a question of who has the nearest hand, but that by the PF calling it, and the PNF doing it, the loop is closed, and both Pilots know that the Autopilot is engaged.
Its one of those 'routine' things that you get used to doing a certain way perhaps, and it then feels right .. but I still think it makes the most sense.
Ultimately, every action on the flight deck should have a logical basis, not just a "Ah sure whatevers easiest".