The information I posted below ( now changed to red ) is wrong as it applies to the 4514 not the 4518
Your engine has a self energizing magneto with a hall effect trigger module contained within the magneto coil
Thus what you think is the primary power feed to te coil is actually the ground wire that goes from open circuit ( running ) to ground ( stopping ) .
IF you tried to test the coil by flicking 12 V across that wire then you have destroyed the hall effect trigger chip and the coil ( now called a module ) is ruined
If you did not try to energize the coils, remove the kill wire and crank the engine
If you get a spark then the magnetos are fine if you do not get a spark they are toast .
Check the wire with the brake on, drive in neutral, PTO off & key switch on it should be open circuit ( to ground ) and should go to ground the instant any one of these happens
1) blade switch gets turned on
2) brake gets taken off
3) key switch is turned off .
IF you have cooked the coils, double check that in no configuration of the controls battery voltage shows on that wire
The coils for your engine will come up as NLA but you can fit the latter model coils
They are wider so you will need to make up a longer stud to fit the coil & blower housing on and fit a slightly longer bolt on the other side
Note these are handed left & right .
The left hand one goes on the left hand cylinder as viewed from the drivers seat
I have a mixed pair on my mower , original right & later coil on the left