I have a similar problem with my 04 V8. I have not left it for 3 days to take a voltage reading, but overnight the voltage will go down to about 12.3v.
One method I have found helpful is if you get access to the fuse boxes on both sides, open both passenger and driver side doors, engage the locking latch on the doors so it thinks the doors are closed and lock the touareg with the key fob. Now you can let it sit for at least two hours so it will go into "sleep" mode. After two hours it up take a reading off each of the fuses with a DMM, if there is current then that component is consuming electricity. If you are lucky you can find a constant draw and fix it that way.
The problem is that some components can cycle on/off over a period of time and may be off when you are testing the fuse. The only way to find out if one of these components is causing the draw is to test with an ammeter(which are very expensive, especially when you are dealing with mili-amps) hooked up for a number of hours.
This is basically where I am in the whole process - nothing found so far, I will probably have to take it in to get it figured out.
Hopefully you will have better luck.