odibrom
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I'd go with start from scratch and transform this pickup in a 4 wire one. You'll free the bobbins' START and END leads and that's where you should measure the coils' continuity.Or I can keep it and just try to fix it and use it. I can convert it into a 4 wire conductor cable instead of the braided wire.
Oh, can you record some clean, and crunch tones? That could give us some clues as well, because to adjective sound only goes that far...? (you're doing great, but I'm still unsure about a reverse phase or a coil not working at all)
The thing here is, the more we ask of you, the more difficult it will be to return the pickup if in fact there's a broken coil... in that situation, maybe a re-wiring to original specs on a local builder?... yeah, I know, more money thrown into it...