Having given initial ME CIR training, flown GA twin charter (line + C&T), and multi-crew turbine ops over the last 5 years I have seen many different briefs.
One of my instructors gave me a fantastic lesson about asymmetric flying: "There is a big box, and a little box. The big box is flying the plane, the little box is cleaning up a failed engine"
Yes it is important to clean up a failed engine in a light twin, but that counts for nothing if you still hit the trees. There is a lot of talk about Vyse with little mention of Vxse
If an aircraft is under control (the FIRST priority), then the next threat is terrain!
Why not get away from it in the most efficient manner possible? Go for max AoC until clear of immediate obstacle threats, then accelerate to Vyse until above a 'safe' (circuit/msa/lsalt etc) altitude.
I believe that a touch drill is essential in the early stages. I still encourage it for anyone with less than 500hrs ME. As for the brief, it must in my view/experience include what you're going to do before your decision point, what you're going to do after your decision point and what you're going to do for a normal departure.
For further nonsensical reiteration, this is what we do where I work now:
We rotate at the recommended Vr and with positive climb (Positive RoC on VSI, Increasing Altitude on Alt and ground falling away) we climb at Vxse until clear of obstacles or 400ft AGL and then accelerate to Vy.
As such our brief is:
If I have an engine failure before positive climb I will....
If I have an engine failure after positive climb I will..... (insert your touch drills)
Acceleration altitude is e.g. 1600ft
Climb gradient required is e.g. 3.3% (from SID) which = XXX fpm at Vyse
Otherwise normal departure will be.... e.g. @ 1800ft, left turn to intercept 263 on climb 6000', 10MSA is 3100ft, LSALT is 3400ft [AS PER SID]
Are there any questions? [if flying two crew or dual]