JSFiddle - React, Tailwind, and code Playground

HTML

<div class="dropdown">
  <span class="dropdown-label" style="display:block">Select a thing</span>
  <ul class="dropdownItemContainer">
    <li>Item 1</li>
    <li>Item 2</li>
    <li>Item 3</li>
    <li>Item 4</li>
    <li>Item 5</li>
    <li>Item 6</li>
  </ul>
</div>

CSS

ul.dropdownItemContainer .hovered {
  background-color: #FF0000;
}

JavaScript

var dropDown = document.getElementsByClassName("dropdownItemContainer")[0]

document.addEventListener("keydown",function (e) {
    if(e.keyCode == 38 || e.keyCode == 40 ) {
        var key = e.keyCode
        var hovered = dropDown.getElementsByClassName("hovered")
        if(hovered.length != 0 ) {
            cur = hovered[0]
            cur.className = ""
            cur = cur[(key==38?"previous":"next")+"ElementSibling"] || dropDown.children[key==38?dropDown.children.length-1:0] 
        } else {
            cur = dropDown.children[key==38?dropDown.children.length-1:0]
        }
        cur.className="hovered"
    }
});


dropDown.addEventListener("mouseover",function (e) {
    for( var i = 0,j; j = dropDown.getElementsByClassName("hovered")[i];i++)
        j.className = "";
    e.srcElement.className = "hovered";
});
console.log(dropDown)