Question: Someone moved a very important page on my website into the trash, and I do not know who did it! It was not deleted permanently so I don't need to worry, in that sense.

The revisions, when I restored it, show that someone edited it 3 days prior to today, so it could have been them, but I can't be sure.

Does WP keep track of who clicks the trash button? If not, I presume I'd have to write a custom script to hook onto the trash button, when clicked.

Answer: 
By default, no, WordPress doesn't keep track of who changes post statuses (at least that I can see).

you can hook into `transition_post_status` and log the user id.

```
    add_action( 'transition_post_status', 'wwm_transition_post_status', 10, 3 );

    function wwm_transition_post_status( $new_status, $old_status, $post ) {
     if ( 'trash' == $new_status ) {
      $uid = get_current_user_id();
      //somehow or another log the $uid with the $post->ID
     }
    }

```
WP can not do it, but you can go to the server logs and find the user's IP. It may take some effort and success is not guaranteed but this is the only possible way. Will's answer will help you in future mistakes.

Finding a user based on their IP is not usually hard especially if the number of authors is limited.