Alright.... I have some development of this issue. FOR THIS MOMENT IT IS SOLVED FOR ME, BUT DRIWING LONG TERM TEST IS PENDING
This morning I came to car and it started right up but run for like 10seconds and died. From that moment same story - cranking fine but no starting up.
I tried to measure all kind of leads and fuses again with no luck.
So in desparation I started to move cables to and from fuse box and I did aply presure to plastic cover on the bottom side of a fuse box in attemps to perhaps move some wires and or connectors to possibly restore conductivity before I disassemble it or perhaps order new fuse box.
Also I moved connectors in the area including some control unit which is beside the fuse box.
And car started right up.... No clue why so I kept tinkering.
So I found following:
-> While car is running I disconected fuel hose coming to the fuel filter (to remind I have 1HZJ 4,2l turbo diesl). I was expecting some stream of fuel, but non was coming out. Engin kept running for some 10-15sec befor it slowly died from no fuel. So I reconected hose and pumped few times with hand fuel pump. And engine cranked few times over and came back to live. Im surprised as I expected pump to be going and steady and perhaps slow fuel flow, but nothing. Yet engin is running and I also tried to load it for some misutes to like 3/4 rpm and it goes fine. Runing in idle for 10minutes. No sighn of any hickup. So despite no strong fuel flow it is going fine. I dont know if there should be presure or not, but car is running at least for this time no issue and there is no presure.
-> So I went to tinker with cables while car was running to see if I move it and perhaps disconect something again. Nothing happen as I tried to move cables and push again on bottom of the fuse box. Car running strong not even short chocking or slowing rpm.
->So I begin to move conectors and found that as I touched and moved just a little with that conector from that control unit engin sudely died. So I tried starting and it was dead again. So I wigle that conector on that control unit for a bit and apply some conductor spray, cleaned inside and reconected. Car started right up. So I tried to move that conector again and after moving some milimetrs towards unpluging car died again. So I think I found it. After some testing I found also it happens when you disconnect it replicate check engine light same as happen to me before when engin went out during driwing. If you plug it in and start engin immediately then check engine light goes off after few seconds. I dont know if this is solution for me for 100% as also it could happen that I restored some conection while moving those other cables and or pushed on the bottom fo fuse box. I will see and update here if there will be some development for me.
->Still I have a feeling this might be my problem as that engin went out just by only touching that conector initially. There was probably some cold conection. I will see on long term driwing.
-> Also for EFI relay draw was initially 4A and dropped to 1,6-2A. I had multimetr connected for 10minutes instead of fuse and draw was consistent while car was running.
->I tried to attach picture of problematic connector and also that unit. Perhaps it will help to someone. I still dont know what that unit is and what for, but clearly it kill engin. I will figure it out once I get time. If someone know then please let me know here.
Good luck