How much "shake" at idle is acceptable?

Not enough cam for it to shake. I agree with what has been suggested that could be wrong.
Ha, May be it's cold and has the chills. The OP may never find out why without a lot of knowledge and some sophisticated test equipment. To the OP, do you have anyone close that has a diagnostic oscilloscope and knows how to read it? If you don't you may never find it unless you just happen to stumble upon it. (or throw enough parts at it for it to go away).

I am guessing it is only at idle. ??? Lean? Who knows.