A recent post at a sister site Best field remedy for small cockroach in the ear has an answer that says
A few drops of baby oil (light nontoxic mineral oil) to suffocate the cockroach then tweezers to carefully remove it once dead and motionless.
This seemed unlikely to me, in the given scenario I suspected the baby oil had an additive. Per this link "some roaches can go up to 40 minutes without breathing" further suggesting suffocation was not the cause of roaches lack of motion.
I have done some more research and it appears this does actually work as described.
Doctors Settle Cockroach-In-The-Ear Controversy The proper way to remove a cockroach from someone’s ear, it seems, has been the subject of little-publicized disagreement. The time-honored method is to drop some mineral oil in the ear, then try to pull the little critter out. A newer, competing technology is to squirt it with lidocaine, an anesthetic, to make it bug out on its own. Source
Both solutions above were ultimately successful. They found the lidocaine more effective.
Lidocaine does have draw backs as outlined in this article
Cantrell removed the dead roach with a set of alligator forceps, but the patient complained of dizziness for five hours after leaving the hospital.
"It is known that topical anesthetic agents entering the middle-ear cavity can be absorbed by the oval and round windows and cause vertigo," he said. The oval and round windows are parts of the middle ear used to transmit sound. Source
Putting aside which is the more appropriate choice. I just want to know how the mineral oil kills a roach quickly when it normally takes up to 40 minutes to sufficat one.