Presumably you completed you MEP training prior to the IR course as they are seperate courses!
EFATO always looks at the "worst case" take the single engine EFATO and the PFL, how many practice partial power failures? There is an assumption, that if you can deal with the worst case you should be able to contend with a lesser problem. A good instructor will demonstrate alternative scenarios.
In the case of the twin, the essential element is CONTROL, without SPEED you cannot control the aircraft; without POWER you will descend rapidly so you need as much POWER as you can handle. If you can't handle, it CLOSE both throttles and land ahead the asymmetric problem has gone away. You do not have TIME on your side.
There is no point identifying, if you are not under control! Then it is essential to ensure you tidy up the dead engine and minimise the drag to aid the PERFORMANCE because you are probably still descending. Identification of the correct engine (Use your feet) and identification of the correct levers is very important hence the deliberation brought inrto the drill. Two RAF C130 crashed during EFATO practice resulting in a major rethink of the way things are done.
The drill you are learning, is to teach a sequence, if it ever happens for real you will fly the aeroplane; move all the levers forward; by now you should know which leg is dead, Identify the levers - throttle first to verify- feather, feather feather; Gear Up Flap Up, bank to the live engine and see if it will fly away! If not, you may have to resort to plan B!
Many light twins will not climb away from an engine failure close to the ground at low speed, be prepared to kill the asymmetric problem by closing the throttles and land ahead, it requires thinking about before you go, there isn't time when you are struggling to control the direction.