SHtml.ajaxCall allows to execute some JS (its first arg) and pass the result as a parameter of its second paramter (hence the String => JS signature). 
So I would remove the sectionId parameter of visibilityCallBack, then give as first param of ajaxCall the correct JS to get the section ID ( something around $(this).closest("[id]").id ), and barelly change visibilityCallBack JS function to use its v parameter in place of the sectionId one.