Taxonomy page wpml dropdown not working

The default language selector is pretty crap TBH.

I created this function using jQuery, you will have to amend to fit your template.

function language_selector(){
    $languages = icl_get_languages('skip_missing=0&orderby=code');
    $current_lang = ICL_LANGUAGE_CODE;
    if(!empty($languages)) { ?>
        <div id="language_list">
            <div class="current">
                <img src="https://wordpress.stackexchange.com/questions/95978/<?php bloginfo("url'); ?>/wp-content/plugins/sitepress-multilingual-cms/res/flags/<?php echo ICL_LANGUAGE_CODE; ?>.png" alt="<?php echo ICL_LANGUAGE_NAME; ?>" /> <?php echo ICL_LANGUAGE_NAME; ?> <i class="icon-chevron-down"></i>
            </div>
            <ul>
        <?php foreach($languages as $l): ?>
                <?php if($l['active']) continue; ?>
                <li>
                    <a href="<?php echo $l['url']; ?>"><img src="<?php echo $l['country_flag_url']; ?>" alt="<?php echo $l['native_name']; ?>" /> <?php echo $l['native_name']; ?></a>
                </li>
        <?php endforeach; ?>
            </ul>
        </div>
        <script type="text/javascript">
            $(document).ready(function(){

                var languageSelector = $('#header .additional .language');
                var currentLanguage = $('.current', languageSelector);
                var languagesSelection = $('ul', languageSelector);


                var toggleLanguageSelector = function() { 

                    if( !languagesSelection.is(':visible') ) {

                        currentLanguage.addClass('active');

                        languagesSelection.slideDown(300);

                    } else {

                        currentLanguage.removeClass('active');
                            languagesSelection.hide();
                    }

                };

                currentLanguage.bind('click', toggleLanguageSelector);

            });
        </script>
<?php
    }
}

Then implement like so:

    <div class="language">
        <span><?php _e('Choose Language', 'theme_text_domain'); ?></span>
        <?php language_selector(); ?>
    </div>

Try this and see if it works, obviously I will leave the CSS to you.