No idea. The park lights come off the headlight switch, and they all use the same switch. Some guys move the park wire over to the tail terminal on the HL switch, and that causes the park lights to stay on with headlights. There should be NO connection between that and anything else, unless someone has done some hacking, or if you have had a short and melted a harness
Dell is correct above. Back in the day many owners would find various ways to get parking lamps or running lamps to be on at all times. And you may be correct in assuming the ignition switch was tapped for this purpose.
I don't recognize the relay, nor have I studied its need toward the goal. I can't think of a reason to not leave it as you found it either.
I'm going to put some thought into it though. If the park lamp circuit is infact fed 12 volts from ignition switch, then park lamps are pulled on at the headlight switch you have 2 of 12 volt circuits feeding the park lamps. That may not be a problem but... lets look at when ignition switch is off and park lamps are pulled on at headlight switch. Now you have a 12 volt back feed to ignition switch that will either feed 12 volts to multiple circuits or blow a fuse. The properly wired relay would prevent that back feed.
