When I press the gear shifter even with the car off, it lets me shift anywhere from park to drive but shouldn’t the shifter not move if the brake pedal isn’t pressed?
I also noticed when I press the gear shift button the little thing inside the housing goes in but I included a video to see. I looked on diagrams and on the forums here but I can’t find it. Thanks!

 

These cars have no interlock between the shifter and the brake like a modern car does, but they DO have an interlock between the shifter and the ignition. That unit you show is supposed to be mounted to your ignition switch, to keep you from being able to shift into Park unless the key is in the lock position. It also prevents you from turning the key to the lock position unless the shifter is in Park......

 

Thanks that actually helps a lot and would explain some other issues😂