I would say that you're definitely onto something if the reluctor ring on your new engine has twice the number of teeth as your old one does ..... which makes me wonder what engine you actually have as the "twelve tooth" ring seems to fit every Mk1 Jazz engine I can think of according to the component suppliers websites ....
If you think about how the ECU probably works, it will almost certainly use the camshaft TDC sensor to determine the instant the engine gets to TDC and as there only seem to be 12 teeth on the CKP ring, then it probably uses the CKP sensor pulses to determine how fast the engine is rotating, in other words the RPM.
On a petrol engine, the instant of delivering the spark is critical ( compared to a diesel engine where the instant of delivering the fuel is critical) and the spark ignition point will vary hugely depending on rpm, load, temperature, throttle position etc. The brilliant fuel economy of the Jazz engine is very much a function of getting the right amount of correctly vapourised fuel ignited at the correct time to allow complete burn and maximum energy utilisation.
As the CKP ring has only 12 teeth, it can't really be used as an accurate enough position sensor to determine the number of degrees before TDC that the spark needs to happen ( I'm used to shaft encoders on industrial machines that often deliver 360 pulses per rotation, but going much slower in general).
Given that there are only 12 teeth on the ring, the best resolution that can be achieved by using it as a position sensor is a very coarse 30 degrees, which can't be good enough to determine the spark point, so I assume that the TDC sensor supplies the TDC postion and the CPK sensor pulses allow the ECU to calculate the RPM and then the ECU uses that information to calculate the "TIME after the last TDC" to introduce the spark.
Obviously if your ring has 24 teeth, then it would probably immediately send out an error as the ECU would be seeing twice the number of pulses from TDC to TDC and would twig that something was up as the data was "impossible".
I would imagine that it might possibly still try and spark, but, as you rightly say, the spark would be completely wrong as the ECU would think that the engine was rotating at twice the RPM that it was actually doing?
Having said all that, I have no idea of the function of the "double tooth" on the CKP ring, unless it's used as an indicator to say that the ring has done a complete rotation. On shaft encoders that I've worked with, there is normally a "channel B" that pulses to indicate TDC and allows the controller to reset the "channel A" pulse counter and start counting from zero again.
I'm pretty sure you're right, but would love to know what that engine is ..... a rare 1.5 perhaps?