[Buster Brown]

I do not know what is causing the shaking but I would recommend getting the testing done because if ignored it could get worse. Perhaps get pet insurance before it is diagnosed as a preexisting condition but I would not put if off.
When he is playing with the stuffed animal if he is burying his face into it he may be breathing heavier to get more oxygen since the toy is blocking his nose mouth.
Buster also hates the smoke alarm. Dogs hearing is more acute than ours and they can hear higher frequencies. The pitch of an alarm is extremely loud and high so it is more painful to a dog than a human. Plus they do not know what is going on only that there is a loud painful noise, the people are all excited and waving things. He is not sure what is causing the problem so he attacks the rag because it might be causing the noise and upsetting the people.
Remember the old saying. LET SLEEPING DOGS LIE. This saying came about because people woke dogs up by touching them and the dog not knowing what is going on reacts to what is attacking them. You will see some people react the same way if they are startled awake by someone they may lash out before they are fully awake.
These seem to be common reactions of a dog but the shaking is not, please go in for further testing. Best wishes to you. You have an adorable dog!
ps I was just thinking does the shaking occur after flea/tick medication since it seems to happen every couple of weeks? Just wondering?