mossback: I'm not entirely certain that a DMM is the correct tool to measure the electrical damping characteristics of the shock. The problem with the DMM is its sampling rate in comparison to the likely wave shape from the shock (which I would suspect is mostly symmetrical with a fast decay time).
If possible, I suggest that you use an oscilloscope - preferably one with a trace capture capability. I've no experience with this type of measurement, but the low impedance reading suggests that the signal is current based, rather than voltage based, so measuring into the shock with an open circuit probably isn't the best idea (if you have disconnected the wires from the module). Instead, it might be more prudent to use a shunt load of some type and then measure the volt-drop across the load (i think). If I remember my lab professor's teaching (long ago now), the maximum energy transfer happens when the measurement impedance equals the transducer impedance! So, if you measured the 1.3 ohms with the shock connected, it's likely that the latent internal impedance of the shock is 2 x 1.3 = 2.6 ohms (because the transducer would be wired in parallel with the low impedance of the module. So consider a 2.6 ohm shunt resistor as the starting point for your measurements (I think)
If you can't get access to a storage oscilloscope, then you might try an analogue ammeter, but you will need to take account of the inertia of the coil/needle in the meter vis-a-vis the time constant of the electrical trace from the shock (I think). If you have not disconnected the shock from the car, then an analogue volt meter might be better than a DMM (but the mass-inertia of the needle and the frequency response of the meter is still a factor in the reading)'
Don
PS:
"I was a bit surprised, the shock generates small amounts of AC current in the millivolt range but No DC." Is this so surprising? The typical waveform of the shock would likely be something like this:
As you can see, the waveform is largely (but not totally) symmetrical - so when measured by a "true RMS" reading DMM. it would register an AC value, with little if any DC component - I think!