I did a little searching and found
this article that seems to describe the Toyota ignition systems and indicates that the "ignitor" is the same as the ignition module. The pickup coil sends a signal to the ECM which then sends pulses to the ignitor, and the ignitor provides ground to the coil primary to cause the field to collapse and fire the spark plug.
If you happen to have access to an oscilloscope you could pretty confidently verify if the issue is the pickup coil, the signal from the ECU, the ignitor, or the coil. These pulses will be too short in duration to be picked up by a typical multimeter.
-Rod