The link below is to the wiring diagrams for the Nav/Entertainment system. Ten amp fuse 58 shows on pdf page 3/12 and from there, one can hopefully follow where it all goes. This pdf has over two thousand views and perhaps a similar number of downloads.
https://disco3.co.uk/gallery/albums/...tem_wiring.pdf

I admire your attempting to get all going as it is not easy - one has to be very patient.
The above pdf link is part of a larger file that I made up related to the Nav/Entertainment system when I was having trouble with the radio going silent. My problem or solution related to finding the mute pin on the radio head and applying power to it to make noise happen. I wondered if that was what the wiring mod you discovered was all about.

My fix, powering pin 10, does not make sense however as most mute pins work by being grounded or not. The pin number was 10 on connector C2115 on the Harmon Kardon High End audio head and had to have +12VDC power run to it full time, or at least when the infotainment system was energized. This is anytime the engine is running. Also I call pin 10 a mute pin but that is me; perhaps it something else and just seemed to be a mute pin.
Also my Bluetooth system uses 2121 as a pairing code number. What bluetooth system you have affects the wiring to the audio head. The attached doc shows pin numbering related to the Bluetooth installs, 0000 & 2121.

This is the link to the file with all the downloads - most of the individual files have a thousand views, hence there are some who think the material has value.
DISCO3.CO.UK Photo Gallery - NAV Radio BlueTooth phone and Rosen DVD

Also I assume that you have done what I call a hard reset. It does no damage to the vehicle and sometimes is what it takes to get the radio making music again. Basically, the hard reset drains all the capacitors that are retaining software memory and forces the software to reload fresh. It is kind of the same as Control Alt Del on a computer. The hard reset instructions are attached in the doc below.

As I said, getting the infotainment system working is a patience thing but learning how it works will pay off over the long run.

 

Thanks to @bbyer and @DakotaTravler for the good info.
I have gotten the power to the nav by jumping the number 5 relay, and the Nav screen came on with the LR logo. However, I have replaced that relay, but it didn't change anything in normal mode. So it's not the relay.
What is happening is that the radio will come on for 20-40 seconds and then shut down. It holds presets and time, so I suspect that whatever is causing it to cut out is not cutting all the power. Ultimately my hope is the head unit is bad. Having followed much of the testing up to the 14 minute mark of this video - - my experience is tracking with his, except that mine is intermittently working rather than being totally dead.

After pulling the head unit out and poking around in that area, I now suspect that someone had an aftermarket unit and other things in the truck. The harness has been respliced to the connector on the back of the radio. And it's tight. But the connections seem solid. Thinking that there has been another unit in the truck gives me a bit of hope about the head unit being bad. And if I can get another one running, it may lead me to an aftermarket setup. (But I am not ready to go to that without knowing the wiring is actually working. Let's not chase that rabbit here).

My hope is that the head unit is bad. That would explain the relay not activating, the steering wheel controls not working, and the cycling on and off. However, I fear I am not going to be that lucky. It doesn't ever seem like it's easy for me and the truck.
But assuming it is $500-1000 when I pull into the Rover shop, I may take my chances on a returnable Ebay head unit and see what happens. If it works, great. If it follows the intermittent pattern, then I will know it's the wiring. And if it does something different, I will have an extra stereo to throw out of the garage in frustration.

 

I must say you are persistent and your logic is good.

I mentioned Bluetooth in the previous post and will elaborate a bit. With a Bluetooth connection between your cell phone and the entertainment system, music comes out of the speakers until someone phones. The radio mutes and phone call ring sounds come out of the speaker - only one however it seems - the little one in the left driver door by the exterior mirror. What I am suggesting is make certain that you do not have any sort of Bluetooth powered anywhere near the vehicle as due to some odd ball reason, the radio is muting due to it thinking a phone call is in progress or something.

Also the radio sounds etc are somehow connected to the entry courtesy lights and also if the key is in the ignition or not. Often with the car locked and sleeping, pushing the key fob unlock with light up the Nav display for a while - usually not the radio however. Basically circuits are being powered or depowered and this affects the operation of the entertainment system.

I also spoke of doing a Hard Reset. For me, if the battery has been disconnected for some time, (usually while installing a new battery), the radio will not make music noises. The phone Bluetooth would function and if I recall properly, the CD player as well.

If fact, you might try and play a CD and see what happens.
What I am getting at is that there are so many mute and sleep circuits in the vehicle, it is a wonder the entertainment system ever worked.

For me to get my radio working after I converted from the factory analogue Bluetooth to the factory fibre optic Bluetooth, to get the radio to work, I had to apply full time power up the pin 10. I have always wondered if this was effectively a workaround rather than the correct fix. It worked and the entertainment system is still working well years later, but I still wonder.

Regarding relays, there are very few conventional relays of the plastic cube variety in our 3's, but the circuit boards are full of what are called FETs, Field Effect Transistors, that act as relays. A FET is not good for more then a few amps and that is one reason there are so many conductors in our vehicles - each power window is on its only circuit etc and the entertainment systems has a number of power inputs all subject to the on/off ability of the FET. If there is any good news, for the most part, and yes, very odd, most of the circuit boards in our 3's are very reliable.

The problems are usually conductor related or a plug is partly disconnected even when it appears fully in place. LR made some of the power cables maybe an 1/8" too short, hence some of the plugs always have a disconnect pull on them. The one big cable plugging into the rear of the speedometer housing is subject to this problem and the backup memory chip for the whole vehicle is mounted on the speedometer circuit board.
In other words, unplugging and plugging that connector can solve any number of problems, including even something like the fuel needle reading oddly - that or temperature can be a hint of a connector partly disconnected. Also that connector can cause the vehicle not to start as the car needs to see both the backup and main chip that is located on the circuit board on the rear of the glovebox located fuse panel. That is also why you cannot replace the speedo circuit board with a junkyard board as the VIN number coded into the backup chip must match the glovebox chip located VIN number and software load.

 

Thanks again for going further into this. I, conceptually, understand all of it, thanks to the explanations. However, I still lack the experience to dig much further. That said, I have an update.

I had done several hard resets as I had commandeered the entire garage for July and much of August. They didn't resolve the issue.

Seeing what you said about Bluetooth, I decided to check those modules in the back today, and, well...ugh.
As I started to pull the panel, I found mouse droppings, but not recent ones. Then, as I got the panel down, much to my surprise, there was no Bluetooth module. It had been removed by a previous owner. I never bothered with trying to connect my phone because I didn't use the truck that much. I used Alexa Auto, and it did all I needed until the radio and nav went blank in July.
I now wonder if mice were a problem that led to the removal of the Bluetooth module. A previous owner replaced the head unit with its own Bluetooth and modern amenities, and when they went back to sell, they kept their stereo and put the oem one back in. That's my working theory now. And to be clear, there is no indication of recent mouse activity. This was old stuff.
The person I bought the truck from only owned it a year ( I now know why ) and he used the stereo as is with an aux cord. He was either clueless about some of what was wrong with the truck, or he sold me up the river. I prefer to think he was clueless and cutting his losses, rather than he was an as-----le.

But I know now that Bluetooth is not the cause of this problem. And the hard reset didn't help.

Given that this all started after the truck was parked outside for two weeks in June, it leaked and got really humid in the heat, for this week I am going to lean into a component failure, rather than a connection problem. I think it's worth a try. And I think that it's like the head unit that is not sending power to the nav. It will power up, play the radio for 20-30 seconds, and then blip out and shut off. The MOST infrared goes after the music stops and is making it to the amp below the passenger seat.

A different issue I now want to figure out is where the MOST network goes after it leaves the amp below the passenger seat. And what has been taken from the original system?
But for now, the focus will be to try to get what I have working before exploring what's not there and what I could or should do next to make the thing reliable enough to drive regularly.

Thanks for the help and encouragement. I'll report more soon.