JSFiddle - React, Tailwind, and code Playground

HTML

<ul id="myList">
  <li>One</li>
  <li>Two</li>
  <li>Three</li>
</ul>
<button>pew!</button>

CSS

ul {
  list-style-type: none;
  padding: 1em;
}
li {
  border: solid 1px gray;
  margin: 5px;
}
.selected {
  background-color: orange;
}

JavaScript

$('#myList').on('click', 'li', function(){
	$(this).addClass('selected')
    .siblings().removeClass('selected')
})

$('button').on('click', function(){
  $next = $('#myList .selected').next()
  if ($next.length) {
    $next.click()
  } else {
  	$('#myList li:first').click()
  }
})
$('#myList li:first').click()