OK, I think you're going to have to bite the bullet and start doing continuity checks on the Engine ECU and CODE Immobiliser ECU wiring. If the CODE Immobiliser ECU cannot talk to the Engine ECU then that is one reason why the CODE light in the instrument cluster will remain illuminated (or why a constant +12v is present on pin 2 of connector A as in your case).
I think it will also help your cause if you find out why the CODE light isn't illuminating in the instrument cluster so you don't need to keep messing around with a multimeter to see whether or not the CODE light is illuminated. The problem isn't with the CODE Immobiliser ECU because you are getting 12v from pin 2 of connector A so it must either be with the wiring between the CODE Immobiliser ECU or a problem with the CODE light circuit inside the instrument cluster. The first thing to do is to check continuity between pin 8 of connector A (pink & black wire) on the CODE Immobiliser ECU and pin 8 of connector B (pink and black wire) on the instrument cluster. Connector B is on the right-hand side as you look at the instrument cluster from the front
shows it from the rear). If there is continuity you will know the problem is inside the instrument cluster, otherwise it will be due to the pink & black wire being broken wire somewhere.
To check the communication wire between the CODE Immobiliser ECU and the Engine ECU, check for continuity on pin 8 of connector A (white & green wire) on the CODE Immobiliser ECU and pin 16 of connector A on the Engine ECU (pinouts for the Engine ECU are HERE
Also, if you haven't already done so then check that there is a permanent 12v on pin 18 of connector A of the Engine ECU and 12v on pin 8 when the ignition is switched to the MAR position. For those last two voltage checks, it is important that you put the negative lead of the multimeter on one of the bolts that is holding the Engine ECU to the throttle body.
If you think any of this is starting to get beyond your capabilities then it might be worth thinking about getting an auto electrician out to check everything over for you.