Too much wax................shimmers???
Motor mounts maybe but no clunking right?
If you put trans in neutral is shimmy less
Vacuum gauge is very very easy to use on any engine, and costs about $20
It can tell you ALOT about engine condition and if there is a problem.
Read here: Technical Articles: Engine testing with a Vacuum Gauge - at Greg's Engine & Machine
I assume check engine light works, but is off when engine is running, so no trouble codes