You asked about pet reincarnations and the following came to my mind. Recently one of my Tiger cats went missing and I am pretty sure something happened and he is no longer alive. I have noticed that his twin brother who has a completely different personality, has started displaying similar social behaviors like his brother. He has started playing with the dogs, playing with one of the younger cats, interacting more with people and even started laying on his back like his brother did. It has made me wonder if animal spirits can come across through other animals.
Dianne