The purple wire is the 12V return feed to the battery.
It can go to a few places.
To an "A" terminal on the ignition switch ( switched )
To the hot wire on the starting solenoid ( unswitched)
Spliced in before the fuse on the power feed to the ignition switch.
So if you have a battery warning lamp it most likely goes to the lamp or to an A terminal
JD has a habit of using a "Fuseable link" wire to splice this into the ignition switch power feed wire ( one that goes to the B terminal.)
A fuseable link is a fancy name for some wire that is only just able to carry the full power ( 12 A on a 15 A alternator ) so it melts under heavy load.