The coil with the red and green wires may be broken. However, it may also only be a bad solder joint on one or both of these wires. You can carefully remove the tape around the wires (not around the coils!) and measure the resistance where the wires from the pickup join the wires from the four conductor wire. If you get a reading there it's a bad solder connection. Reflow it and you should be good.
If you don't get a reading, reflow the solder connection of the wires coming from the pickup that are attached to the red and green wires. Do you get a reading now? If yes, it's alive. If no, it's dead - get it rewound or part it out.
Not long ago I had a pickup that measured dead but when I resoldered the connections it came alive.
Cheers Stephan