Both, really. The connection is always active, but your awareness of it changes.
When you actively pay attention to it, then it’s going to be louder and you’ll notice it more. Your chakras (like the heart chakra) respond to that focus, and you’ll feel the intensity physically.
But the connection is still there, even when you’re blocking it out and focused on other things. Even when you’re not thinking about them at all, that energetic cord is transmitting information back and forth. The spontaneous pain is when something breaks through your normal filters - maybe they’re having a particularly emotional moment, maybe you’re in a relaxed state where your ego isn’t blocking the signal, maybe your higher selves are communicating in the upper dimensions and your physical body is registering it.
There are physical pain signs of reunion as well, but (as @Cassady said on that thread too) just take care of yourself.