Changing the brake light switch is a PITA! It's behind the brake pedal and takes a little patience to change out. If the car is under warranty, take it to a dealer. There were 2 recalls on brake light switches. I changed the first on myself and took it to a dealer the next time because it was such a chore to change out!

 

OH... good... so at least now you know that your cat is not playing tricks on you and you'll be keeping the poor innocent feline. LOL j/k
I love hearing stories where a car owner saved lots of money.

 

Yes, it's happening to my Audi 2004 A4 again, now that the weather is cold. Why only at night and (for me) only in the winter? Theory: It has to do with how the temperature affects the brake fluid. (In other words, it's not that it's night; it's that the temperature has dropped.) I think cold has a slight compressing effect (as heat would cause expansion) and possibly the loss of vacuum pressure works to pull the brake pedal down enough to trigger the brake lights. I can't think of any reason why an electronic part would care about the temperature. (My problem, at least, has only happened in the winter.)