That's the one I was referring to, and how I would do it if it was my job.
No. The red wire is your signal (hot/positive etc) and the back plate (or even the cover) of the pickup is going to be connected to ground (negative). That's why you get continuity at the green or bare wires. They are connected to the ground of the pickup.Btw should there be continuity from the red wire to the back of the pickup (I don’t get any) like I get from the bare wire to the back of the pickup?
Here's a screenshot of the wire colour code:
It may help you visualise how HB pickup wiring works.
Note: the bare wire is not shown in the diagram.