My feeling is that it's very unlikely that the rear light has failed. Most likely the connection. I've posted a thread here about how I fixed that on my own bike.
Are you at all handy? The first thing I'd do is open the plastic plugs at the back of the fender and check with a voltmeter if there is current there. I'd bet there isn't. And if there is, I'd try to re-seat the wires from the taillight carefully and check the light again. I'm on my iPhone at the moment or I'd go and find a link to my thread about improving the wiring. It was only a week ago. If you can't find it, let me know.
The way Giant has made the wiring connections at the front and back of the fender is really poor. That's probably what your issue is.