Describing the ECU as an amp is not exact. Yes it has a transistor that pulls the coil (-) to ground, but the interface to the reluctor sensor does not resemble an amplifier. The interface rejects the negative swing of signal, then triggers at a point a few tenths of a volt above the zero cross transition. The pickup signal amplitude increases proportionally with engine RPM. The cranking signal with too much reluctor to pickup gap, signal ampitude is too low, and may will result in no start. It may have been running well at idie before shutoff, the signal at idle 3 to 4 times greater than cranking signal.