One of the more challenging things to teach in ab initio training is how to prepare a low time student for an EFATO. As +TRSA pointed out at post 32 outcomes that relies on a cognitive decision making process at a very stressful time are likely not to work with very low levels of experience. I want the student to if time permits, to shut down the engine for 2 reasons. It forces the mental shift from "I am trying to restore power" to " The engine has failed and I will concentrate on flying the airplane to a survivable forced landing" and second it will stop the potential of the engine starting at an in opportune time. I know of one case where a pilot had the engine fail at about 1000 ft. He had continued straight ahead to a smooth field off the end of the runway. As he started to flare the engine roared back to life he started to climb away and at about 200 AGL it failed again. He ended up crashing in to trees at the end of the field wrecked the airplane and was very fortunate to avoid serious injury.
Al that been said the flow to shut check down the engine is the same one to determine a cause of the engine failure. If the engine fails at say 900 feet and after establishing a stable glide the pilot actions the shut down flow and finds the fuel already off, then it would be reasonable to turn it back on. The important point is 1000 ft AGL to landing is 60 to 80 seconds. A lot has to happen in that very short period of time and spending a lot of time trying to get the engine going is likely to detract from flying the airplane which has to be the primary focus.
Fred.Kite
I am always looking to steal better ideas. Please describe what you would teach a 15 hour student to prepare them for an EFATO ?