The coils is just a transformer - low voltage in (lots of coils) high voltage out to jump the gap and make a spark.
One side of the coil input will be the source and the other side will just be a connection to ground - the chassis of the machine - it will not matter much where or how this connection is made.
I know nothing about lawn mowers and precious little of motor car electrics.
Good luck...
Peccavi
April 2013