Car in question is a 1993 Mazda Miata with 1.6 liter engine.
Right after I start the engine the RPM drops below idle and the engine shakes a little bit but quickly recovers. After I give it a very small amount of throttle, barely a touch, the RPM also drops. Sometimes, but not always, after holding the throttle at a certain RPM and letting off the gas the RPM's would drop.
As well, after the engine has been running for a long period, at least a half an hour, when the car is stopped the engine would "shake" every 10 seconds or so and I can feel it in my seat. It is not as violent as it sounds.