It is something to consider, I will keep picking at it until I get it figured out. Your variables are very well named.
var rotation_active = true by default in your code
Our main question to ask is, if it is the last list item it will be within the var you created below I believe to make rotation_active = false.
var start_automatic_rotation = function() {
rotation = setInterval(function() {
if (rotation_active) { rotate_quotes('forward'); }
}, rotation_speed);
};
