Airports with obstacles after initial takeoff and clean up have special procedures. TGU you would die for sure if you flew RH either north or south until clean up because of terrain. Engine out takeoffs can be quite interesting in RNO and TVL orbiting a hill on instruments. Never just fly runway heading unless you are in FLA or MN where there is no terrain thinking you are safe longer then you have to.
Bogota has the most complex engine failure procedure depending on when you lose the engine I just tell the FO we will just return and land VFR. Unless you are based there it is unlikely a briefing would help anyway because of all the changes depending on when it happens. Yes, if it is IFR you have to do it but with unlimited visibility a waste of time.