You must have missed the part that the person who provide the fix I quoted earlier ([xj-s] 94 V12 Volt/M on dash drops two nw when pressing foot brake) is in the UK and has a RHD v12 coupe.
This is not it. Perhaps you car being a TWR-modified beast is more important in that regard.
It does have a few small changes to the wiring harness, most notably is an extra chassis harness that runs to the rear to run the two fuel pumps and a different connection into the ECU. I don’t know if that would require a change to the socket that is causing the problem seen with the brake lights, or change the power distribution to be different so that it us under less stress.