I'm fairly certain that I discovered today that they are linked to your use of actions. I was kiting a fate boss that I was soloing for about 30 seconds waiting for my chocobo to heal me. He didn't do anything but run with me for the entire 30 seconds even though he had been healing me before. I started throwing my spear at the boss and every time I did, my chocobo would heal me.
Can't cast while running. And it run if you run on healing stance.
