I agree with Cholla in a sense: I believe the pickups send a ground though. The 12V should (IIRC) be a constant from the igniter, as T Cro pointed out. I don't remember a connector between of the igniter and the coils, but I agree, check it out, because it has been a LONG time since I looked at this.
I have a spare igniter or two if you need one to try out (and maybe purchase, not sure why I have 2).