Okay, I've updated this answer. The tooltip now appears when you focus/click on the input field. You can click any item in the tooltip and it'll not disappear. When you remove your mouse from the tooltip, it'll disappear.
I think that's what you wanted.
$("#genre input").click(function(){
$("#genre #vor .overlay").show();
});
$(".overlay").mouseover(function() {
$("#genre #vor .overlay").show();
});
$(".overlay").mouseout(function() {
$("#genre #vor .overlay").hide();
});
/*$("#genre input").keyup(function (){
//For Testing
var text = $(this).val();
$("#genre #vor .overlay").html($('<div id="item">'+text+'</div>').click(function(){
$("#genres").append("<span>"+text+'</span>');
}));
});*/
.overlay::before {
border: 6px solid transparent;
border-bottom-color: #FFF;
border-top-width: 0;
content: "";
display: inline-block;
left: 10px;
position: absolute;
top: -5px;
z-index: 101;
}
.overlay::after {
border: 7px solid transparent;
border-bottom-color: #CCC;
border-top-width: 0;
content: "";
display: inline-block;
left: 9px;
position: absolute;
top: -7px;
z-index: 100;
}
.overlay {
border: 1px solid #CCC;
display: none;
float: left;
padding: 5px 10px 5px 10px;
min-width: 25px;
position: absolute;
z-index: 200;
box-shadow: 2px 2px 10px 0 rgba(0,0,0,0.2);
border-radius: 5px;
top:4px;
left: 5px;
}
#vor {
position: relative;
height: 0px;
}
#item {
background-color: #474747;
padding: 2.5px 10px 2.5px 10px;
border-radius: 8px;
margin: 3px 0px 0px 0px;
color:#FFF;
cursor: pointer;
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div id="genre">
<div id="genres"></div>
<input type="text"></input>
<div id="vor">
<div class="overlay">
<a class="clickItem" href="javascript:void(0)">Item 1</a><br />
<a class="clickItem" href="javascript:void(0)">Item 2</a><br />
<a class="clickItem" href="javascript:void(0)">Item 3</a>
</div>
</div>
</div>