As mentioned before, testing a coil pack with a multimeter actualy tells you nothing more than the coils are ok, it fails to identify the common coil pack failure mechanism and gives zero guarantee that the coil or coil pack is ok......in short, its a poor test!
Lets start with the basic operation.
As you already state, the positive side of the coil primary is connected to 12V when the ignition is on (note, on some cars its via a resistor which is shorted out during cranking so as to maintain high coil volts when starting.....so not always this simple!). The negative side connects to the points or electronic ignition system (note the condenser is a transient suppressor to minimse arcing across the points contacts so treat it as a secondary item rather than a primary par of the operation).
When the engine is cranked either of the following happens;
1) A cam rotates in the distributor which opens the points
2) An electronic pickup is triggered to give a timing signal, an electronic switch then 'opens' in the same way as the points.
The basic operation of the coil is this.
When the points or electronic switch are closed current passes through a coil of wire which is wrapped around an iron core (you can see the core on some coils and on the V6 dis pack). As this happens, a magnetic field is 'induced' (created) in the iron core which effectively acts as an energy store.
When the points or electronic switch open, the current flow stops and the magnetic field in the iron core starts to collapse. The energy from this has to go somewhere but there is no longer a circuit on the primary (the points/electronic switch are 'open circuit') and so a current is induced in the secondary winding (this is wound onto the same iron core).
The secondary winding has many more turns than the primary which results in a much higher voltage (due to the turns and a little bit of theroy called V=L x (dI/dt) which is a little complicated for most unless they have excellent maths
) being produced.
This gives a spark of many 10's of KV.
All very simple and the modern systems work on the same principle all be it with more coils and no distributor to distribute the spark to the plugs (distributor is repalced by electronic switches).
A few pointers:
1) The time that the points/electronic switch remain closed is reffered to as the 'dwell angle', this is actualy the time available to induce the magnetic field in the coil and in the case of mechanical systems (e.g. points) is related to the points gap at maximum opening and hence setting the gap is important (you can get dwell meters which measure the dwell). Electronic systems do this 'automaticaly' by monitoring the curret through the coil. If Dwell is to low, the spark energy will be less (less magnetic field 'stored' in the coil)
2) Testing coil output requires a special test plug with adjustable gap, when removed from a compression cycle, a spark plug will only need a few thousand volts to spark.....this is NOT a good test method......and the screwdriver to the head is also not a great science either!. As a guide, a spark will generaly jump around 1mm for every 1mm of gap!
3) Its a weekly moan of mine regarding 'Earths' as earths do not appear on cars and it is an incorrect term. A key reason why I harp on about it is because 'Earths' are very important and critical to safe operation of many electrical items and hence need care and respect. A vehicles body is a 0V point or a chassis return, to make it an earth you would need to connect it via a large metal cable to a large metal spike driven into the ground
. In summary, when working on a real earth (e.g. house wiring etc) you need to treat it with great repsect and care as the fault current it may have to handle can be 100's of amps plus even on a low current system where as a chassis retrun could be as simple as a screw through the body work which is man enough to carry the operating current of the device.
On the lawnmowers, they are probably a magneto ignition switch with a capacitor system.