Now I am really confused
Are you saying when you pull the black wire with the white plug that is just under the left side of the coil off you get no spark and when it is re-connected you get a good spark ?
It should be the other way round, or a good spark both ways if the safety switches are all working as they should .
Please check that black wire
It should be closed to ground with the key in the off position & open with the key turned on .
Also check it for voltage there should be none in any key position .
So as I see it ( and there are a lot of things I have never seen ) the mower has a faulty coil