This sweet Lady was holding a very young bunny on her lap, and here you can see her gently massaging its ears. I can tell you she sat there at that same spot for at least an hour. She was in Heaven.
We brought a crazy jack russell to visit my aunt when she was failing and past speaking and probably past knowing who anyone was. Tiger jumped up on her lap and sat ever so quietly (not his usual manner at all) while she petted him and murmured all sorts of confidences to him as he listened attentively. It was wonder to behold. These pictures remind me of that visit.
I never knew rabbits liked their ears massaged. But I do know that any animal that will sit and allow itself to be petted is a comfort to the elderly. My cousin brings a visiting dog to the nursing home near her on a weekly basis. It's not her dog, but a dog specifically trained by the animal shelter for that purpose.