What happens if I Blink while my Familiar sits on my shoulder?

My lizard Familiar (from the Find Familiar spell) is often sat on my shoulder. If I use the Blink spell, would it shift with me to the Ethereal Plane, or would it be left behind and splat to the ground back on my original plane?

There’s nothing in the text about things you’re carrying or wearing travelling with you, but presumably they do to some degree. I assume taking another creature would be too much.