Now that wasn't that hard or do you need some pain killers?
View attachment 72618
Now since the voltmeter and temp gauge works then problem is either a bad solder joint on the circuit board, bad light switch, bad bulbs, broken wire, bad socket terminals or any the wire terminals in the light circuit.
Black wire runs from circuit board to the light switch to the light sockets. Provides +12 volts and current. The green wire is the ground return circuit. Provides the -12 volts and current return path.
Simple circuit that you only need a test light or volt meter to trace the circuit.