Something I personally feel like would give the pets a bit of extra touch is, if they would actually move and look around on their own, without being in the same area around you all the time.

It's always a bit... emersion breaking when you go into the third person and see how f.e. the Will o' wisp is always looking in the same direction as you while sticking in the same place around you.

The behaviour could simply be the same as f.e. a Dog as in moving around, but always staying near you and going towards you if you move away.
(You could perhaps even use a modified version of the dog API for extra laziness? Idk... I don't mod)