Where does the hose that comes out of the back of the water pump go and how do you replace it when it leaks?

I had to look at this question for a minute because you didn't say what year model we are working on or what engine size. But I guess we must have a 1996 or newer model, and we must be working on a 4.6 liter engine. If I am right about what we are working on, the bypass hose you have described, goes through a valley under the intake manifold, and exits at the rear of the engine, where it connects to a heater hose at the firewall. It is partly rubber hose and partly metal pipe, but it is made as one assembly. To access and replace, you must remove the intake manifold. After the intake manifold is moved out of the way you will see it clearly. At the back of the engine, on the right cylinder head, there are two bolts that hold it to the back of the head. There is also a bracket that is held to those bolts by two nuts that are screwed to threaded studs that are part of each bolt, so that you have to remaove the nuts, remve the bracket, then remove the studded bolts, and then remove the bypass hose/pipe assembly, all of this after you have removed the intake manifold.