We used to have a dog named Peabody many years ago. Each night, my mom would let Peabody out before bedtime to do his business one last time. He'd go out and do it, then when he came back in, my Mom would reward him with a Milk-Bone. Eventually, Peabody learned that he could finagle an extra Milk-Bone out of my mom by pretending he needed to go out again. My mom would let him out because she didn't want to take a chance that he might really need to go again. Peabody would run out to a bush and lift his leg for a couple of seconds without really doing anything. Then he'd turn around and come back in, and get his second Milk-Bone.

I don't know if I'd call it a ritual per se but a breed trait ours want to be in the middle of whatever is going on. If you're putting together an Ikea shelf put them away or they want to be in the center "helping".
If you're laughing at something they get excited and want to be in on the joke, smiling and sort of "laughing" with their entire bodies. If they think you're laughing at them they try to replicate whatever it is they thought they did to make you laugh offering all kinds of behaviors.

I've taught a few things just "naming" something they were doing. Once it was "lick your lips" while eating yogurt. Of course it took them no time to figure that out so when any of us would have yogurt from then on there they were "licking their lips" in front of you. LOL

I've been working my Labs in obedience and other dog sports for quite a while. It sounds like something you might be interested in. I just looked on the AKC website and the local obedience club is (or was) the Fort Worth Dog Obedience Club. They don't seem to have a website, they might have folded. If you check the web, you might be able to find out what's going on there. Or check the local breed club, those folks might know the story.

Anyway, the obedience and rally obedience sports are a lot of fun and you learn a lot about how to train your dog for a lot of different things. There's also agility, where the dogs run an obstacle course for speed. The newest AKC sport is nosework, where the dogs have to find certain scents that are hidden. There are lots of dog sports out there, check them out, you might find something you really enjoy.

My two dogs both rescue have their individual games and my one dog when in the car likes for my wife and I to sing, I really don't know why . It is great to see their individual personalities. We just love animals of all kinds.

I learn so much off of my dogs and far more than I teach them.

I have and have had border collies for years I don't get to be the one inventing the games or setting the rules that is their job; mine is just to play and obey them.
I exploit this ability to invent game to use them to move and control cattle but, in doing so I always have to remember that they make the rules and I have to follow them. One of the rules that drives me crazy is that one of them, Pepper, has to cut out of the last animals going threw the gate so, she can chase it down and bring it threw the gate without the other or me interfering. Should anyone try to help she will force a repeat of the game.

We have two cats: not much into games, but plenty of rituals.