This is so eerie. A similar thing happened to us a month after my Bubby O”H died. She was nifteres on Purim and on Shabbos Pesach, on what would have been her 87th birthday and also was the day of her Shloshim, a beautiful black and white dog came into our yard and would not leave. The particularly weird thing about this is that whenever my Bubby was in need of a blood transfusion (because of her fatal disease of the bone marrow), she would periodically begin to hallucinate for a couple of days, and always saw a black and white dog sitting under her sewing machine. P.S. because the dog exhibited incredibly smart and charming qualities, we who would NEVER have considered having a dog in our home for any reason, alowed him to become our cherished family pet. He was a phenomenal watchdog, and incredibly loyal to us. We always felt that Bubby had sent him to take care of us when she was gone, as she herself had taken care of us (she lived with us) for the last thirty years of her life.
I don’t know about the gilgul part, but it’s really fascinating when an animal shows up suddenly, won’t leave, then attaches itself to someone.