Before we got our boys, I had never had a cat.
I think our boys are demanding. I love them dearly, and I enjoy them more than I can say but they need attention.
D needs about an hour of 1:1 attention every day. And I do mean EVERY day, alone, with me only, not Mike present (who he loves and needs the same exclusive interaction with), not another kitty so much as watching. And he is an F5.
Jarvis needs to be with us. CONSTANTLY. From the moment we get home until the moment we leave. When I lock him out to socialize with D, he lies in front of the door and waits. NO MATTER HOW LONG THE DOOR IS CLOSED. If we don't pay attention to him, and play, he scratches the furniture (it is the fastest way for him to get our attention, not something he actually enjoys we think- he only does it when he wants us to pay attention to him). Jarvis is an F3.
Mickey is an F4. He can't sleep through the night without one of us. Minus both of us, if we shut him out the little guy paces all night. We have our special time in the morning. When the Alarm clock goes off, he comes up, lays between us, and we pet him and snuggle him for 20-40 minutes (depending on the day).
And this is with THREE savannahs.
All three will use the litter box without us, but if we are home, they are with us. Not just in the same room, but within 10 feet. 24/7. All of them use the litter boxes in the morning, when we are in the rooms with the litter boxes, with them, and again at night, when we are in the rooms with the litter boxes with them, so that I completely understand.
When we come home, they know the sound of both cars, and they meet us at the door. Savannahs, in my limited experience, need affection, and interaction. Constant interaction. Even if you are spending several hours with your kitty, he may just be missing you badly when you are not home. Our boys are friends, and we go through an "oh good, you are home, I MISSED you" scene, BOTH of us, every night. And that is with three boys from the same breeder who play together and who clearly are friends (they cuddle and groom each other). I hope that helps.