@Andrew Hughes: So why don't you use it as a feature? Hovering and pressing the button opens a floating menu with variable options. For example:

Center: Pen
Up: Eraser
Down: Swap between Color 1/2
Right: Selection Tool
Left: Geometry Tool

While the button is pressed, the menu appears under your pen, you hover over to your selection, release the pet's button and the menu disappears. When get used to it, this could become an intuitive hover flick for many users. You then could also augment some of those four sub-menus by more selections. For example:

Up-Left: True Eraser
Up-Right: Other eraser of which I forgot the name.

Or for the colors a palette of 6 pre-defined colors all surrounding bottom half of the icon.

The floating menu could easily be done using Google's Material Design. The icons just like the new edit-button at the bottom-left corner in reading mode. The central icon as bigger bubble with the app's blue, and four smaller bubbles at each side. Each bubble containing the icon of the tool.
When pressing the button, after a delay of 100 ms all 5 bubbles pop up centrally under your screen. (Delay for avoiding unnecessary animations when doing a flick).
When hovering over one bubble the others's alphas decrease and the selected onbubble gets 100% alpha, or it gets highlighted by a shadow, or both combined. Then, if the button gets released, the other icons fade out quite instantly and the chosen icon zooms in (rising up or "out of the screen") while fading out, but for a much longer time.

For the sub-sub-menus to be seen, one could hover over the base tool and after a delay of about 250 ms, the sub-bubbles appear, which are yet smaller. And when choosing the base tool next time, either the standard-tool is used, or the last one.

Finally a double click could be "reading/editing mode".

And for all supported devices: Clicking and touching the screen as scrolling. Or fast erasing. Or gestures. Like press and left for 'Undo'.

Sorry for sounding like telling you how to do your job. It's just my imagination of it that I had for so long. I loved the idea so much, I was often wondering how to realize this. And this is just my idea of it, wanting to make you realizing this easier. (My thoughts even went so far, last time I started to research whether it is possible to manipulate the values in the RAM of other processes in Android to build my own app for this, when I realized I could just ask the developers to do this).

Really: This feature would make this already great app an even much greater app. :)

You're absolutely right sir... The button only works when the pen is hovering above the screen... But I use this without any problem nevertheless... Please make the button compatible with your app so that I can use it regardless if the pen is close to the screen!!!

This feature works as intended on the Note 2 (N7105). But I'm currently running Cyanogenmod 12.1 (Lollipop) so I don't know if that makes a difference.

In the FAQ it says this isn't possible. But other apps such as Lecture Notes support the pen button