I assume when you say you have continuity at the transformer that the 2 coils have continuity too.
The magnet could be weak, does it attract an object liken a screw driver?
Another cause may be the vane driving the pin to the cone may not be centered between the two poles of the coils. To fix this I usually shim both sides of the vane to get it centered. You then have to adjust the pin where it connects with the cone. Sometimes there is an adjusting nut. Other times the pin is soldered to a small metal piece in the center of the cone. In that case I just heat the connection with a soldering iron and solder. When cool remove then shims. The vane should remain centered then.