If you want to show the background change of #Home or #About when hovering only on a then you can use the following:
HTML
<ul id="NavList">
    <li id="Home"><a href="Second.aspx">1</a><div></div></li>
    <li id="About"><a href="Second.aspx">2</a><div></div></li>
</ul>
CSS
#Home,#About {
    position:relative;
    width:70px;
    height:50px;
}
#Home div, #About div{
    position:absolute;
    background: url('https://i.stack.imgur.com/2JzQz.jpg');
    background-position:-20px 0px;
    top:0px;
    width:100%;
    height:100%;
}
#Home a,#About a{
    position:absolute;
    top:20px;
    left:20px;
    z-index:100;
}
#Home a:hover+div , #About a:hover+div{
    background: url('https://i.stack.imgur.com/7rx8G.jpg');
    background-position:-20px 0px;
}
Got this idea from How to style the parent element when hovering a child element? .My CSS is different but using same idea.