Controlling an analog automotive tachometer

BenF:
Note however that the signal on the negative coil terminal is a complex waveform that looks nothing like a 12V square wave.

Sometimes they will pick up a 12V square wave, sometimes you need to put an induction coil in the circuit to produce a high enough spike for them to pick up. A 12V relay coil (with the switching hardware removed) does the job nicely.