[bazar01]

On a healthy engine with no vacuum leaks, the idle behaves rough, the same way as yours if you remove the oil fill cap on top of the valve cover. This replicates a big vacuum leak. Does your engine behave the same way?

We had the same problem before after replacing the valve cover gasket and spark plug round grommets due to oil filling up the spark plug holes.
Came to find out the valve cover gasket was not properly seated on the back side. Had to take the valve cover back out and reseat the gasket. The idle smoothened out after that.

Your oscillating idle is a big vacuum leak.