I think Hand 1 doesn't really invite a bluff. He could have all kinds of underpairs that have showdown value - so he doesn't need to bluff, but he will pay the river with them. If he has a flushdraw - what can he put you on that you would lay down if he bets?

There are other situations where I would check to induce a bluff, like a 568 QA board - I would check-call the river there a lot with middle pairs.
On less obvious boards I probably want a read that the opponent likely has a draw, and is capable of bluffing if I show weakness.