Great links,
Qsilver7...
It looks like the positive power to the third brake light connector (X138) is a single continuous wire, right back to the LCM. My next test would be to check if there is power between the black/yellow wire (X138, pin 2) and a known good earth point, as the issue may be with the earth connection rather than the power connection (as the earth connection has more joints).
Clearly, you need to test this with the foot brake applied!
