I haven't opened my Pokémon Go Plus yet.
What battery does it have inside?
I was thinking of buying a battery later.
According to this article (specifically, point 13; "Do I need to charge the Pokémon Go Plus?") the battery inside is a CR2032 lithium coin cell. The Plus's battery life is estimated at 100 hours of use, so if you use it frequently - start stocking up.