The mystery was solved this morning. As 4ePajero said: Did you check the earthing and 12V cables??

It was the negative terminal clamp on the battery - too loose, even when tightened all the way.
When the struggle initially started I had the old battery (sold and installed by auto shop A) tested and they found 2 dead cells, so it was replaced with a new one with the same type and make under guarantee - again sold and installed by auto shop A.
They guys installing it did not see that the clamp was too big and did not fit tight enough, so it was loose and that is where the needed juice went.
Presto.
I assumed they knew how to install a battery. Just as others assumed I had the common sense to FIRST check the earthing and cables. At least my EGR valve is now cleaned and I know what my glow plugs look like.
Dankie oom Gerhard!
Will keep an eye on it today and tomorrow to see if the solution is lasting.