I have friends and relatives who live in NJ and have heard the horror stories for years. NJ's propaganda service has done its job well, as most have no idea what is or isnt legal, and the misinformation and rumors fly freely, even amongst people who live there.
When my kids got into grade school here they thought NJ was not part of the US, as I always told them we were leaving the country we we crossed the bridge.
In all the years I've been going across the border, I've been stopped quite a few times, all for mostly BS excuses of a reason, but I've was only ever ticketed once, which actually amazed me, especially when you talk to those who live there, who seemed even more amazed. A couple of the times I was stopped, I was on my way to shoot in matches in south Jersey, and I kept my mouth shut about what was in the car. They never asked, and I never offered. I probably would have said no if asked, I know someone from PA who answered honestly and didnt have a very pleasant experience. A word of advice, dont leave anything gun related, like a live round, laying in plain sight.
Its not out of stater's that need to watch themselves, I personally know of two NJ residents who had their pistols confiscated, even while following all the prescribed "rules", for transport and behavior, or at least they thought, silly them, you have to shoot at an approved range, and not in a sand pit in the Pine Barrens. Took them almost a year, and a bunch of money for the lawyer to get them back.
.....notification is only required if you are carrying.
As far as I know, unless something has recently changed, this isnt a requirement in PA. I never told them anyway, even when they asked about the bullet holes in the back of my truck. He had to go back (after he walked by them the first time), and put his finger on the stickers, and boy was he mad! We had to wait for back up and everything before he'd even get out of his car. Jeez, the cops in W. Conshohocken have no sense of humor!
Needless to say, they came off right after that. There was no way I was going into NJ with them on there. But I did bring a few and put them on some other peoples cars.