I never did get the hang of Chaperone (perhaps because I hear people call it "Chappy" and there can be only one). When you use it, are you aiming for headshots or body shots?

Both, depending on the situation. I use an Eyasluna as my primary weapon and the sweet spot for aiming is the same. Right about where the collarbones meet. Should land you a headshot most of the time. That being said, there is an extended range for the Chaperone where a headshot isn't lethal but a double body shot IS. The gun fires quickly enough that you can get that double tap off before a fusion rifle charges or before the opponent is in shotgun range (fire while backpedaling against onrushing shotgunners).

The double-tap is also effective against juggernaut titans - you can pop their shield at extended range and then OHK them in the face as they cross into your kill zone. Just aim for center mass and let the kick carry you up.

Of note: I've been playing double smoke and grenade / no super nighstalker with this, so I always have a soft AoE up which means the chaperone body shots for lethal more often than not. Because the range is superior to other shotguns, you often find yourself tossing smoke around a corner, tagging the enemy, and then taking a wide angle to get the single shot kill while staying out of range of their own weapon. Very effective.