Read more does not show up when I write my own Excerpt

Perhaps a conditional statement like the following will work. The logic is: “If the post has an explicit excerpt, add a read more link. Otherwise, use default excerpt behavior.”

if($post->post_excerpt) {
    the_excerpt();
    echo '<a href="'.get_permalink().'">Read More</a>';
} else {
    the_excerpt();
}

You can use this in combination with Gavin’s suggestion to unify the appearance of the “Read More” link.