I've unfortunately STILL not got the bottom of this issue...
As before, this seems to be an issue only after wet weather, so today I fully removed the LCM (brief guide below for others trying to do it), it was bone dry so I cleaned all the connections as @kds suggested. Then with it removed I poured water all over that side of the car as a test, but having a good feel around where it would be (and right up inside the dash) I couldn't feel any water or wetness....so it doesn't seem like water is getting into the cabin. Having said that, my previous fixes to the wiper tray haven't been 100% as water is still dripping down inside here (see pics below).
Now with a clean and dry LCM reconnected....the lights are still all over the place! Argh! Indicators working sporadically, headlights & rear lights flashing when on, and it's currently sitting switched-off but with slow indicator flash!
So, I'm now guessing the issue isn't water getting onto the LCM specifically, but onto something else (wiring, other unit etc.?) and that's what's causing the issue.
My plan for tomorrow is to again try to seal under this wiper tray to stop the ingress here....and then cross my fingers that stops it.
Any further help / advice people have would as always be appreciated. E.g.

1. Does the above sound logical?
2. Any ideas what the electical box in the pic below is? (The one with a yellow & blue cable coming out.) As that's definitely getting wet so could be the issue?
3. Are there any other key pieces of kit that could be causing this strange light issue?

Thanks in advance...and I'll let you know how tomorrow goes!

<<<
My Guide for removing LCM:

• Silver RR footplate pops off with a screwdriver.
• Cover around the bonnet release will then slide backwards, so you can see the LCM and wires going up to it.
• I then removed the bonnet release handle to improve access (3 torx screws hold it to car)
• Then there is one bolt at bottom of LCM which needs to be removed - but the top ones doesn't, it just slides out downwards.
• Three connectors can be tough (top & bottom have a slide mechanism to hold them in, middle a white 'handle' which comes up & over).

>>>

So after all of this I *think* it's finally fixed! Big thanks to Merv at Autoelectron (details below), who I wish I'd known about a few months ago.
Basically, I think that at some point there had been some water damage to the LCM, but this then came & went over the next few months - apparently, once it's damaged, it can be months between it playing up, and behave find in between. Having now had it fixed and refitted for a couple of weeks, all seems to be well so I'm keeping my fingers crossed.

Merv can be found at: http://autoelectron.co.uk/index.html. He also has an ebay listing (https://www.ebay.co.uk/itm/283844982047) but go direct to save money. Fantastic service too; I spoke to Merv and posted the unit on a Friday, and it was back fixed by the following Friday - at a cost of under £70!

I don't believe in coincidences , but this is interesting.
https://www.landyzone.co.uk/land-rover/transport-mode.372335/page-3