Where is it located ?

The coolant amplifier is a little whitish plastic box located next to two relays on a a relay tray right at the middle behind the dashboard but before the windscreen. You'll access it by removing the top roll.
Source: Diverse

How to test it ?

Here is a "cut and paste" from an article by B. Vogel :
You can do this in the boot/trunk of your car.
1. With the switch turned off, hook your power supply cable to the battery. Connect the alligator clip from the positive lead to the +12V pin on the amplifier (RED on picture) and the negative lead to the ground/earth pin on the amplifer (NEGATIVE on picture). 2. Connect one alligator clip from the test lamp to the warning lamp pin (GREEN on picture)on the amplifier and the other alligator clip to the ground/earth pin on the amplifier (NEGATIVE on picture) (or to the alligator clip on the power supply cable that’s connected to same – you just need to have a ground connection with this lead somewhere, it could even be the chassis of the car). 3. Slide the male slide connector on to the sensor input pin (YELLOWon picture) and submerge the opposite end of the wire in the bowl of water. 4. Connect one end of the remaining “bare ended” wire to the chassis somewhere to create ground/earth. One good spot for that is where the negative battery cable screws on to the chassis with its wing nut. Place the remaining end in the bowl of water, but not touching the lead from the sensor pin that’s in there already. 5. Turn on the switch on your power supply cable. At this time your test lamp should not be illuminated. 6. Lift one of the wires resting in the bowl of water out of the bowl. When you do this your test lamp should illuminate. 7. Turn off the switch on your power supply cable and carefully disconnect everything.
Source: The Rolls Royce Forum - England

Another thread here
http://au.rrforums.net/forum/messages/17001/18623.html?1441116211
Source: The Rolls-Royce Forum - Australia