I believe this is a known problem for oil to leak into the distributor. Will eventually cause oil to splatter all over the distributor cap and will cause an intermittent stuttering or bogging when running cold. When the car is warm, it will run better which is due to better heat for the electrical to run. When running cold the electric will be very low, causing it to bog.

The repair is costly. Aftermarket is about half price of OEM bought at Toyota dealership. I bought mine from a junk yard which I was lucky enough to find one good enough... When I went to the junk yard. I found six Celica. I found all of them to have oil residue inside the distributor cap. I found one that had little oil in it so I bought that one. Installed it and from there it is running great now. I inspected it carefully and the oil must be seeping into the rod into the distributor or the seal leaks out, which would enter through those holes that are exposed. But seem like mine was heavily contaminate with oil inside so I think it is from the inner part of the distributor.

If your running rough in the cold morning check your distributor. Clean it and seal off the hole that is exposed and recheck again. Replace the distributor seal. It is not a guaranteed fix. It may be the inner part inside the distributor. It is costly to fix this small problem.

Look like a poor designed from Toyota factory so should they be taking care of this radical problem?