Good.

Clear codes and run them again, this time for transfer case module (the codes you have originally are for terrain).

 

And if you still can not read the transfer case module, then you need to check the appropriate pins for power, etc. Or start looking at grounds. Basically if there is no corrosion, bad connectors then it starts to end up looking like a wiring issue. I have a feeling this might be something simple.

Also this is an example of corrosion, so be lucky if you have none. They also reference a fuse.
https://www.disco3.co.uk/forum/topic108328.html

 

Still the same. Do you know where the ground are for the module? Also where do they go from the box behind the battery? Straight to the transfer case? Are there any wiring for it on the passenger side foot well? This is just so baffling, that it drove for 3km after it got washed. It’s almost as if water made a short somewhere and burned off a wire somewhere, but where? I never smelled something burning or heard anything, I was just driving, normally, went up an incline on the road and then as if someone put it in neutral. And the dash went crazy. I never found any blown fuses

 

Post 4 covers there ground location. Which to me seems like an odd location given the fact the module is on the passenger side. But really if I were you, I would look at the condition of all grounds in the footwells on both sides. Corrosion can hide, so disconnecting them may be a good idea.
https://landroverforums.com/forum/lr...le-lr3-112518/

Also I FINALLY found the thread on the solenoid. Again, if you have no module activity this is a moot point. But just keep this link incase this solenoid was the original cause of the drop out.
https://landroverforums.com/forum/lr...hooting-86760/

And I will say it again though, check all fuses anyway. I have had the larger ones crack or blow in areas that are not obvious in the little window. So swap with another fuse to be sure.