Here's one possible method.
function isMouseInBox(e) {
var textbox = document.getElementById('textbox');
// Box position & sizes
var boxX = textbox.offsetLeft;
var boxY = textbox.offsetTop;
var boxWidth = textbox.offsetWidth;
var boxHeight = textbox.offsetHeight;
// Mouse position comes from the 'mousemove' event
var mouseX = e.pageX;
var mouseY = e.pageY;
if(mouseX>=boxX && mouseX<=boxX+boxWidth) {
if(mouseY>=boxY && mouseY<=boxY+boxHeight){
// Mouse is in the box
return true;
}
}
}
document.addEventListener('mousemove', function(e){
isMouseInBox(e);
})