Widget is not hidden from Customizer's widget list.

[atachibana]

The added widget on Customizer Widget menu is not hidden from available list.

• You can use is_customize_preview() instead of is_admin().
• You may use the same DOM structures and names even if the shown position is opposite. This is the comment from Customizer's view.
  <!-- For Widget Customizer, many widgets try to look for instances under div#widgets-right, so we have to add that ID to a container div in the Customizer for compat -->

But the rendering and DOM generation timing are different from Administration Screen, jQuery.find() could not find the element.