A primitive element

A <div> styled to look like a button.
It has a 'click' handler, so it is operable with a mouse.
It can be operated with the keyboard because:

it is now focusable(added tabindex="0")
it now has a keyboard handler for space and enter $('.btn').keypress(function(e){goober});

And it is not announced as a button in the accessibility API

A "button"

        
          <div tabindex="0" class="btn fake-btn" style="border:1px solid #ccc;background:#eee">A "button"</div>
          <script type="text/javascript">
            $('.btn').on('click', function() {
              alert('you clicked me')
            });
            $('.btn').keypress(function(e){
              if(e.which===13){
                alert('pressed enter');
              } else {
                if(e.which===32){
                      alert('pressed spacebar');
                  }
              }
            });
          </script>