The output from any coil & magnet set up is dependent upon two things
1) the strength of the magnetic field
2) the speed that the magnet passes the coil
The strength is altered by moving the coil closer or further away from the magnets
As the speed of the magnet passing the coil increases so the voltage increases.
This is one method that the module uses to alter the spark timing.
At cranking speeds the voltage will be very low
Did you test it plugs in or plugs out ?
The 4 V listed is peak at 3600 rpm, not cranking speeds.
Note the manual says RUN the engine, not CRANK the engine for this test.
It also mentions to have fully charged battery.
If you get the same readings from both them then most likely they are fine.
If anything has gone bad it would be the magnet in the flywheel,
Use a pair of thin jumpers connected directly to the spark plug coils.
Hook one up and BRUSH the other past .
If you get a spark then the coil is fine.
The spark will be very weak because when you flick, the dwell time is very short
I use 2 x 9V transistor batteries in series ( 18V ) for this test to avoid the chance of burning the coil wires.
According to the service information the primary voltage should be around 260 V.
The full engine manual will serve you better.
And the best engine manual will be found in the JD technical manual rather than from Kawasaki.
There are 3 variations according to your mower serial number
As for the delay module. it delays the shut down function, not the start up function.
The theory is the fuel shut down solenoid closes first then a couple of revolutions latter the spark stops so there is no unburned fuel passing through the engine into the atmosphere which according to the EPA will cause all life on the planet to die.