Maybe it's 9.3.1, but I've noticed that my pencil automatically starts working with the iPad. In fact, when I touch/pick up the pencil after it's been sitting after a long while (say, over night), I can see the Bluetooth icon flash a bit before I even put it to the screen. And the pencil works right away - even after I've turned off or re-booted the iPad.
Sorry I never mentioned this before, but I just now noticed it.
So, if you're having issues with your pencil, maybe try to reinstall a "fresh" version of iOS 9.3.1 or take it to the Apple Store? Cause I think the automatically working behavior is now the norm/standard and if yours isn't behaving so, then there is something not right.
Marilyn