The time out part is to reflect on the behavior, and maybe even some cooling off time and think time for the parent. I like the Jim Fey Love and Logic approach. Think consequences to inappropriate behavior. Think natural consequences. Example: Wake up late and miss the bus to school? Pay for a "taxi ride" from dad.
I reserve timeouts for times my daughter is being extremely disagreeable when we eat dinner at the table. When she's ready to talk properly, she can rejoin us. I don't even time it. She usually comes back with a new positive spirit.
So. . . won't leave the cat alone? Separate them for awhile.
Need tasks to be done? Find creative ways to address the situation. Not putting toys away? Make up a clean up song or make a game of it. He's not excused from the room until it is done. Be kind and firm. It's all in the tone of voice.
I also accommodate her version of what makes sense. Crayons on the walls? Remind her, and then cover the walls with paper for awhile. Climbing onto the counters? Try to put items the child needs (cereal bowl? cup?) in a special area for him that he can reach.
If the mood continues, I then start reflecting upon diet, sleep, activities, stress, my mood (which kids pick up on). Something may be going on. How's kindergarten going?
Best regards.