My recent purchase is a 2009 (2010MY) Range Rover 3.6 TDV8 facelift. It has a few snags! One is that the top piece of the LH taillight. (LEDs) is permanently on with a .3 amp current draw. The new battery drains in a few days. I would appreciate some help reading the wiring diagram that I downloaded for this model from the Wiki section. The brown/yellow wire which is permanently live at the taillight connector goes back in the loom to “FET-Fog-Rear-LH” in the Junction box central via connector C0583-32. How do I find this? Is it easy to test /replace these FET things? The main lighting control switch seems to connect to this junction box and I have already bought a secondhand replacement switch but not fitted it yet.

Would I do better in simply just disconnecting this lamp at the taillight connector to stop the battery going flat ( ie cut the wire) or put in an inline switch?

My Gap tool says there is circuit short to battery or open for both the LGH stop lamp and turn signal, but the current drain seems to be on the fog light wire.

The car should power down eventually, mine does that as well. It's very faint but does go out eventually when everything shutdown. These cars stays alive for quite a while.

Perhaps also worth checking whether they have the original tail lights in them or some Ebay aftermarket special...

Thanks for that.

The light on my car is on permanently. But your thoughts on whether or not my taillight is genuine made me think: is the voltage to the taillight meant to be there permanently and it is the taillight unit which is faulty. I might check to see what is happening on the other side. I was thinking that the fact that there was a permanent voltage was the fault.

I googled the FET:

WHAT IS THE PURPOSE OF FIELD EFFECT TRANSISTORS (FET)
Many automotive manufacturers are now using virtual fuses also known as "Field Effect Transistors" to protect complex High Speed Controller Area Network (HS-CAN) and modules from high voltage spikes. The concept of a virtual fuse allows the Body Control Module (BCM) to monitor modules on the network for excessive current and turn OFF the VOLTAGE or GROUND and store Diagnostic Trouble Codes (DTC) in memory. When there is no longer a circuit fault or short, the BCM FET circuit will reset - and the module will be reactivated when the circuit is turned ON again . Once this occurs, the BCM begins a cumulative count of faults. FET's are built rugged and can withstand tremendous amounts of high current and voltage spikes. 
Field Effect Transistors operate at 3 levels of protection that can handle anywhere from 100 to 600 faults based on predetermined limits set by the manufacturer. When a fault level of protection  is reached, the BCM module will not allow the FET to reset or "CHECK ENGINE" or "MIL" to turn OFF until a self test of the circuit is passed. When all three levels of protection expires, the FET will no longer reset and the defective circuit must be repaired, and the module replaced.

Reference: Automotive Electricity and Electronics, David M. Jones and Kirk VanGelder, pps. 606-607, 2018..

The hole I am digging seems to be getting deeper!!

There is an excellent description of how the Light Check Module works in the workshop manual, worth a read.

David Range Rover 4.2 Supercharged 2006
Ford Focus EcoBoost 1.5 2017
MG TF 2003

Previous Cars of note
Land Rover Discovery 2
Jaguar Mk2 3.8 - Company car
MG Midget 1974 - Concours