Engine failure on take off
" Climb out is probably the worst time to get an engine failure and the time between 20ft and 150ft is probably the worst. As soon as you detect an engine failure you must smoothly get the stick forward and the gyrocopter into a nose down attitude as quickly as possible, even if initially the nose down attitude seems too great. It is easy to bleed off speed in the flare. The only way to get speed without power is TOO LOWER THE NOSE. This takes skill and a quick reaction"
The reason for lowering the nose after an engine failure on take off is not to enter autorotation (as the gyro is already in autorotative flight) but to gain airspeed so that you can then arrest your rate of descent by flaring to land. If you didn't lower the nose then you will "touch down" (ahem!) with a rather high rate of descent and no means of arresting it.
If the engine fails in normal cruise flight you can more or less keep the stick where it is (depends on the aircraft type) and allow the gyro to enter a zero-airspeed vertical descent - though you'll need to lower the nose and get some airspeed before you reach the ground so that you can flare.
I doubt if many pprune posters would seek to make authoritative-sounding statements about, say, Airbus flight characteristics without ever having flown one. It's one of the odd features of gyros that there are plenty of self-appointed "experts" out there who have little relevant experience.