These lights are spiritual in nature and probably someone who is close to you in the spiritual realm. It is nothing to be alarmed over and should be regarded as a gift. Not very many people have this opportunity in their lives.
In regards to pets I have seen interviews with people who have had interactions with spiritual animals who have been sent to help you heal. They have a very strong ability to infuse a deep calmness on your spirit. I would urge you to allow this "animal" into your home as it will implant a deep serenity within your residence. This again is something that doesn't happen to many people. You definitely have "friends in High Places" looking out for you.
Throw some love into the wind.