There isn't a separate bottle for the rear washer, IIRC. I suspect that what's happened is that the feed from the front to the rear has come disconnected at one of the joins along the way, probably somewhere under the passenger seat. This often follows a spell of freezing weather, when the rubber connections come loose after thawing.
Try it while stationary on a dry day and you should see a little puddle of water forming under the car.