Heaven only knows what is going on there
The spades at the bottom , one will go to ground and the other will only show battery voltage when the key is in the start position .
It does not matter which way they are connected
The ground is normally a short wire that comes from one of the mounting bolts which on your mower looks like a blue wire.
I will hazard a guess that one of the safety switches was not working and the mess down there was an attempt to work around the problem rather than fix it .