The initial test would be to check the resistance of the pickup, unplug it from the module and use a multimeter at the connector - you're looking for 750-850 ohms but it can vary slightly with make. Have you changed the pickup recently? The gap between pickup and spindle lobes which should be 0.3-0.4mm. This effects the signal amplitude and smaller gap means big amplitude which is better. You must also make sure the magnetic strip under the pickup is the correct way up for the pickup make - typically the magnets are marked with a paint stripe and it's stripe upwards, but this is not always the case. If the magnet is upside down the signal generated is inverted which is not good. The signal generated when working is much like the trace in the picture. The amplitude varies with rpm and can easily be 20v p-p at higher rpm. You can check the pickup off the car if you have an oscilloscope (handheld digital one are available these days, but still a different price league to multimeters). If you move a screwdriver across the end of the pickup (without touching it), the pickup will generate a single signal high/low. The amplitude will be low ~0.5v p-p, but the positive/negative transition should be correct.
EDIT - I've not used a multimeter on the pickup when cranking - IIRC at 1k rpm running, the pickup is about 6-8v p-p, so at a guess you may see 1-2v on a multimeter reading AC RMS as the signal is not a true sine wave. If I think about, I'll try it next time I'm out in garage as could be useful if ever stuck by roadside!
