My cat moves around all the time. She has four different nap places. One of them being on my lap or right next to me. I don't have much furniture right now either! Not even a bed, which she sometimes just naps on the covers on the floor. 😊
The twitching depends on how comfortable they are. Even to being too hot or cold can be annoying to them. Obviously sounds do it as well.
Where she finally decided to nap. This was the first time she napped here this morning! It's been there three days now.