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Looks as if that has shorted out and burnt. The lacquer insulation is not there anymore. Did you remove it or has it shorted out by itself?
Tracing that broken line, it appears to head back to pin 7 on that 7 pin black plug. You said you had 12 V on that #7 pin. Check if you get the same 12V before the break. You should get !2V. Then check on the other side of the break and if you do not, then I would solder a jumper wire across the break and re-insulate with silicone RTV or good electrical tape.
As per your diagram, pin 7 supplies voltage to those gauges. I assume item 64 is the gauge voltage regulator that takes it down to 10V.
This is where you use your ice pick test light. If it needs soldering I suggest taking it to someone with lots of experience soldering cuircit boards, etc. Like a computer repair place with an old timer. I fortunately have a friend that used to build those Tandy kits back in the 50s and 60s and is really good at soldering. I have never mastered that skill and actually caught things on fire trying.
Also, if you havent already, contact David at everydayxj.com to see if he has a used one. His prices can't be beat and if something doesn't work he bends over backwards to make it right.