JSFiddle - React, Tailwind, and code Playground

HTML

<span id="dropdown_icon" onclick="runThis()"></span>
<select name="region" id="dropdown">       
    <option value="">Select Region</option>      
    <option value="CS">california</option>      
    <option value="DB">Denver</option>      
    </select>
<br>

CSS

span#dropdown_icon { background: url('https://devtools.movilizer.com/confluence/download/attachments/21992022/ICON_MOVELET_29_2-1.png?version=1&modificationDate=1398243475000&api=v2') no-repeat;width: 20px;height: 25px;margin-left:6em;position: absolute;cursor: pointer;}

JavaScript

// <select> element displays its options on mousedown, not click.
showDropdown = function (element) {
    var event;
    event = document.createEvent('MouseEvents');
    event.initMouseEvent('mousedown', true, true, window);
    element.dispatchEvent(event);
};

// This isn't magic.
window.runThis = function () { 
    var dropdown = document.getElementById('dropdown');
    showDropdown(dropdown);
};