I was taught mostly in the Duchess for an EFATO to Power Up, Clean Up (Gear and feather, flaps and cowl flaps as required) Trim (raise dead engine 5 degrees). A failure at height you had more time to do the Identify (dead foot), Verify (slowly pull dead throttle enough to confim), Rectify (try a restart), Secure (feather dead engine, fuel off etc). And Mayday radio call was only done in a Single if it failed; not in a multi. So big difference for EFATO was not Rectifying or trying a restart and quickly getting to Secure, whilst always still Aviating.
In my flying time I never had a real failure in a twin but did in a Single (glided in no damage). But I also never had simulator training for engine failures which would have been useful as all the simulated EFATO's were done after gear up and usually when reducing to climb power so at 100-200 feet up and predictable when the check pilot would pull the lever. A simulator would have given practice when lower down and gear still down etc.