Where is the auxiliary pump and what is the procedure for testing and removing and replacing?

 

The aux pump is located on the Driver's side of the car, under the coolant expansion tank area, mounted on the frame rail area. You'll have to take off the plastic cover to expose it. You'll also likely have to be flexible enough to actually get the coolant reservoir out of the way enough to clear the pump and bracket out. It CAN be done, but if you're nervous, you can try to do it with removing the tank first (provided you can get the hose clips off without breaking those). I was able to do mine without removing the expansion tank, just taking a few minutes to get to the hose clamps, loosening up things just enough to free the pump and twist it out of the way and get it free.

As far as testing goes, it's pretty simple if you have a 12v supply and some test leads. It's either going to work, or not. A common failure is the brushes in the motor. There's a DIY online (JagRepair.com - Jaguar Repair Information Resource ) on how to replace the brushes yourself. If you're replacing the pump altogether if you can find a known working one on the cheap, it's a ten min job to remove the old, install the new.

Here's a DIY of a change on an older XK. Different mounting location, but gives you an idea what it looks like to find it:

Intercooler aux water pump change