In the 3.8.x\main\plugin-web\pages\services\resources\search_3.3.xsl

All fields should have an unique Id like in the form-search-element-keywords template :

<div class="label"><label for="search-input-{$uniqueId}"><i18n:text i18n:key="FRONT_MODULE_SEARCH_KEYWORDS"/></label></div>

Please add the unique Id to this templates :

• form-search-element-pages
• form-search-element-creator
• form-search-element-format
• form-search-element-publisher
• form-search-element-rights
• form-search-element-multisite