Nezumi.May,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.eps{
color: #FF0000;
background-color: #FFFF00;
}
.block a{
font-size: 48px;
cursor: pointer;
}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var a = $(".block a"),
btn = $(".btn"),
indx = localStorage.getItem("indx");
a.on("click", function() {
a.not($(this).addClass("eps")).removeClass("eps");
indx = a.index(this);
localStorage.removeItem("indx")
});
indx !== null && a.eq(indx).click();
btn.on("click", function() {
indx !== null && localStorage.setItem("indx", indx)
})
});
</script>
</head>
<body>
<div class="block">
<a onclick="vidLoc('2713543',this,'3')">1</a>
<a onclick="vidLoc('2711882',this,'3')">2</a>
<a onclick="vidLoc('2716610',this,'3')">3</a>
</div>
<button class="btn">Сохранить значение</button>
</body>
</html>