1990 Cadillac EL Dorado Idle Speed Control

The pulsing of the ISC can be normal as it rehomes itself. 1990 saw it's problems with fuel injectors, when warm they should measure 15-17 ohms resistance each. If they have not been replaced, there are probably some shorted. A misfire at light throttle can also be caused by an EGR valve opening prematurely. There is also a idle learn and minimum air rate adjustment that is to be considered if you changed the ISC motor. Usually the symptom for idle not learned is a sail on condition, when the throttle is released to coast the vehicle can still maintain approximately 30 mph before settling down. It will even speed the car up if you just slightly accelerate and let off the gas.

It does not pulse fuel when the ISC is doing its extend/retract stuff. I don't believe the ISC after key off is causing you any problem. As long as the behavior is fine when running, speeds are ok at start, and no sail on or stall at coast. The roughness after cold soak could be several possibilities, oil coming from leaking valve guides/seals, injectors bleeding off fuel pressure, coolant in the cylinders, for example. Fuel quality can also bring some cold issues.