I have had several interesting pickups in the shop for repairs lately.
This is a pickup from an Alamo Lap Steel with a damaged coil. I always attemp to repair pickups before I resort to rewinding. If the break occurs inside the coil you are out of luck, but if you can find a loose connection from the start or finish of the coil it can often be reconnected.
Many pickups have a hard bobbin that makes accessing the start of the coil difficult but this Alamo pickup has a soft paper bobbin the can be moved to reveal where the wire lead connects to the coil. In this case the thin copper coil wire had come loose from the lead and just needed to be re-soldered.