With the ECU/DME disconnected that possible short circuit disappears. Not sure if this is how it should be or not.
Pin 54 of the ECU is where this connects to. It measure short to GND when the ECU is connected. When I disconnect the ECU there is no short from 54 to GND. If I check for short to GND for all the other sensors and devices that share the 12V from pin 54, none of them measure short to GND. I am confused.
Probably not related, but I also had a closer look at the piggyback computer that is mounted above my ECU (photo below). I never looked at it properly before but I see that it is not actually connected. The connector has been unplugged and some wires very poorly jammed in the connector to short some pins together (presumably re-connecting some of the ECU wires that were being modified by this unit).
I have found someone with a wrecked E36 who is sending me a cam sensor, crank sensor and O2 sensor, so will have these to try next week.