You may have not seen the youtube video below that was on a thread on one of my earlier links but shows the two different westaflia types which use the OEM type subframe.
https://www.youtube.com/watch?v=mYUxjKXqyPw
The detachable swan neck looking type leave the socket behind that is bolted into the subframe so the socket is visible and there is a dedicated range rover storage box that can be purchased so the tow bar is hidden away in the boot. As this is bolted there is no play in the towbar. This type is also a bit more expensive than the flange type.
I have the flange type which is held into the subframe with a pin and R clip so the complete tow bar is removed and just leaves the socket behind which i then purchased the land Rover blanking plug to hide the hole which you see in my pic below. This type comes with the strong bag supplied and I strap mine to one of the load securing rings in the boot as its too big to fit in the storage box for the other type. As this is a sliding fit into the socket and just held in place by a single pin there is a little play in the towbar but i think they are still perfectly functional for your towing requirements but talk to PF Jones as they are the experts.
Regarding the electrics, you want the Westfalia type again i believe as think you still need the ECU but again check with PFJ. The 2010 range rover did away with the ECU and the vehicle itself was reprogrammed.
There is a link below to a site i found explaining the difference but as i understand there are two types of the older 7 pin, 12N and 12S, the N is for a normal trailer and does all the lights and the 12S was added for caravans that needed a supply to the fridge and reversing lights etc.
The later 13 pin euro type combines both in one plug and socket.
if you already have the trailer and horse box then it most likely will have the standard 12N 7 pin type so match that to the electrics but as i was only going to use mine with a trailer board i bought the trailer board with the 13 pin connector as i may get sad enough to want a caravan one day ( my dad has one)
Towing electrics explained | Mota-Bars towbars, Warwickshire
This is the detachable type complete
without electrics
Range Rover 2005 > Detachable tow bar
This is the flange type complete, on the PFJ site there is a magnify link on the left hand side which scrolls you through diagrams and photo's of whats in the kit
https://www.pfjones.co.uk/range-rover-2005-flange-tow-bar-1.html
You can select the electrics from the drop down list but the kit i wanted wasn't in the list so i chose mine off the separate wiring kits page.
This is the 7 pin kit which should include the ECU
https://www.pfjones.co.uk/range-rover-7-pin-dedicated-wiring-kit-2002-sept-2009-323063300107.html
This is the kit i ordered which is the 13 pin type
https://www.pfjones.co.uk/range-rover-13-pin-dedicated-wiring-kit-2002-sept-2009-323064300113-en.html
As you can see i write the word 'think' quite a lot as i don't tow anything so check with PFJ so you get what you want and they were really good when i dealt with them and the price i paid for the subframe was about the same as rusty old second hand ones from latvia..
The PF Jones site seems really slow so couldn't check the links
Hope that helps