There are 2 animals in our house who very rarely make an appearance. One is a small, slightly scruffy brown dog with a big curl in the middle of her back and perky ears and the other is a slightly aged black cat with rickety back legs and a curious face. They look remarkably like Priscilla and Oberon, but they live in this little silver frame in the corner of the foyer. They only appear when Pris or Obie (or both) are in the corner, but they are VERY playful.
Yes, there is a mirror in the corner, leaning on the wall to be hung at some later date... and the animals love it. Pris dances, Obie prances, they rush it, they pat it, they sniff it, they dart back and forth to see if that other dog/cat will reappear.
So much for the theory that animals can't see their reflection!