How to add_action to reader comment box

First of all this is a fantastic plugin! Thanks
I have a really neat plugin that enables commenters to select "make this a private comment". I found the code here:

https://github.com/reigelgallarde/wpquestions.com/blob/master/privatecomment_new.php

This works great in the front end, but I would like it to also work in the "read more" pop-up of your reader plugin.

How can I add "make comment private" function to the read more pop-up of the reader pliugin?

Thanks - Mark

The add action for the front end looks like this: