I hacked it out by putting the configuration options in a function, passing the tag as a variable and reloading the whole thing. There must be a better way.

function juicer(theTags) {
    var jb = new juicebox({
        useFlickr: "TRUE",
        galleryWidth: '390',
        galleryHeight: '550',
        backgroundColor: '#eee',
        containerid: 'juicebox-container',
        captionPosition: 'bottom',
        showOpenButton: "false",
        captionHeight: 25,
        imagePadding: 5,
        buttonBarPosition: "TOP",
        galleryTitlePosition: "TOP",
        themeUrl: "//bla/blas/juicebox/classic/theme.css",
        configUrl: "//bla/bla/",
        textColor: "333333",
        textShadowColor: "rgba(0,0,0,0)",
        captionBackColor: "rgba(238,238,238,.5)",
        showAutoPlayButton: "false",
        showThumbsButton: "false",
        galleryFontFace: "Georgia,serif",
        flickrUserId: "38123794@N03",
        flickrSort: "DATE-POSTED-DESC",
        flickrImageSize: "LARGE",
        flickrImageCount: 75,
        flickrShowDescription: "TRUE",
        flickrShowPageLink: "TRUE",
        flickrTags: theTags,
        flickrTagMode: "ALL",
        imageTransitionType: "CROSS_FADE",
        enableLooping: "TRUE",
    });
}