Fly the aircraft should be instinctive. More important with a EFATO, where the speed would wash off quickly.
In reality though engine failure in cruise i would/have gone for throttle, mixture forward, carb hot , pump on fuel change tanks, etc. All of this would take about 2 seconds. There would be enough momentum in the aircraft to fly itself even if i did nothing and let go of the controls.
Why sit and wait 10 seconds whilst the a/c decelerates to best glide then another 30 seconds whilst wind and field is selected.
We have an engine getting colder or fuel lines empty.
I admit i don,t teach this.
Usually carb hot, fly a/c, trim, wind, field, key points, then restart.
Because it standardises for EFATO.
Also engine fire, i was taught if fire not out, then stop the prop. by slowing down toward stall speed to stop oil pumping out.
How many teach that.