@kodabasenji It's not FOMO. Your pup is associating you and your partner as his pack. That's a good thing. I just think that your pup is upset because he isn't sure how to behave. He wants to be in charge and he cannot be in charge if his pack is not at home.
Doodle got sick of my little game in one afternoon. Today she cocked her head like she was asking me if I was leaving... I asked her if she wanted to go wait in the car (she knows the word "wait") and she promptly turned and went into my bedroom. LOL
Take your pup for walks and work on commands (like, sit, stop, heel, etc.) along the way. This is two fold. One, he will learn that you are in charge. And two, it will tire him out so that he behaves when you are out of the house. You've got this.