It is not possible to create a new custom button with its own functionality.
However, you could perhaps take advantage of the way that the 'Open Image' button works and re-appropriate it for your own requirements.

Try the following:

• Set every image's linkURL to javascript: custom_function();.

• Set every image's linkTarget to '_self'.

• Set showOpenButton="TRUE" in your gallery's XML file.

• Change the icon for the 'Open Image' button using the technique in the Using Custom Icons support section.

• Change the toolip text for the 'Open Image' button using the languageList configuration option (so as not to confuse users).

When the 'Open Image' button is clicked, the custom_function() JavaScript function (which should be included in the HTML page which contains the gallery's embedding code) will be run.

(Please note that this will not work if using a baseUrl.)

Otherwise, you could create your own HTML button outside your gallery and have it interact with the gallery (if necessary) using the Juicebox-Pro API. (The Juicebox-Pro API requires Juicebox-Pro and is not available to Juicebox-Lite, the free version).