Either be present or be busy, but don't pretend to be both.
I don't know how many times I have been in a meeting - where real work was actually being done - and the CEO or another member of senior management walked in and said "I'm just here to listen". Then that leader went on to look down at their phone and answer email the whole time.
As a manager, you can't do both - you can't be in the meeting and be busy on your phone or tablet at the same time. Not only is your presence unusual that causes people to clam up, but you're a distraction and getting in the way of any work that could be happening.
So, if you're a leader - lead through example. Be present while you are leading.
Notice points in your day where you don't. Notice when you pretend to be present when you're actually busy. Notice when you're acting busy when you're actually bored.
You'll actually get more work done, if you work when you have work to do. And, remember people expect you to be present to hear them, when you say you want to listen.