Glad you have it sussed.

The EGR valve will have had a vacuum pipe like the one in the photo, there are vac pipes running from the solenoid valves on the inner wing that are used on the EGR system. They are usually thinner blue pipes with thicker tube at each end (like the photo) to fit over the EGR valve pipes.

12 light switches, he must have a flux capacitor like in the Back to the future DeLoreon to power them.

Thermostat is in a sealed plastic unit on the coolant pipes at the side of the radiator, it looks like this. https://www.paddockspares.com/pem100990-thermostat-and-housing-td5.html It does sound like you may be getting pressure from a leaking head/gasket into the cooling system, a sniff test can...

The operation is different with modified relay, does yours work like this now.

Dim dip relay may be faulty

The MAF meter measures the air inlet and adjusts the fuel to suit the flow it should default to a mixture that will run the engine when it fails but it needs the MAF to run the correct mixture.

And check the Mass air flow meter. I refitted my EGR and CAT as the exhaust on mine smelt badly and it made a vast improvement, although mine was not smokey.

The low pressure return goes back to the pump high pressure side, putting the return in the tank will not work, the high pressure side will not be delivering fuel to the fuel pressure regulator and injectors, the high pressure side will just be sucking in masses of air from the LP return...

EGR system solenoid

Purge the fuel system a few times, ensure the battery is fully charged and try again. If your battery is not able to spin the engine over fast enough it will not start.

Did it not turn over at all or just fail to fire up. You did not prime the fuel system correctly, you have to turn on ignition and pump the accelerator 5 times to the floor.

Most likely behind the dash, this shows all the headers and connectors but I can't find 291. https://usermanual.wiki/Manual/DefenderTd5MY02ElectricalLibrary.1605721897 Pull the fuse and see what effect it has then you will know what it feeds.

https://workshop-manuals.com/landrover/defendertd5/engine_management_system/relay_main/ https://www.landyzone.co.uk/attachments/defender-02myecu-png.259217/

Who left the door open, once they are in you can never get them out, (only kidding) but agree that the new Defender is such a different vehicle it should have its own forum where other owner can help each other with their knowledge of their vehicles.

Can you not see which number pin it goes into and look on the diagram to see what it is

Look at my post on the link below, the wiring diagram is there. https://www.landyzone.co.uk/land-rover/td5-ecu-wiring-pin-out-list-for-red-and-black-plugs.326182/page-3

Could be for Tachometer, there is a black/blue reference on the list below https://www.mgexp.com/article/lucas-wiring-colour-guide.50

Yes, I was told the same and to buy a genuine Land-rover seal by my screen fitter, even with a genuine one it is a bit of a struggle.