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It is not a propeller what initiates climb, it is an excessive lift from main wing because of increased AoA. (the propeller is there only to prevent losing energy/speed; any glider can go from horizontal flight into the climb in exactly same way as a powered plane). And because excessive AoA means acceleration upwards, in steady climb forces needs to be in equilibrium and AoA at 1g level.
Actually, in the first approximation, for given airspeed, there is only one possible AoA (two if you count stalled region too) for steady balanced flight (straight, either horizontal or climbing/sinking, but not turn). Any different angle will result in excessive force in some direction (lift or gravity) resulting in imbalance. When the flight stabilizes again in new regime, the AoA has to be back at value for 1g-lift.
@EBV821 somewhat not somehow, of course, pardon my English. Anyway, yes, it is not purely vertical movement, but there is still non-zero vertical component and therefore relative wind has to be oriented partially from above too. If pitch with respect to ground/horizon/inertial reference does not increase further, an increase in vertical speed means lower AoA. I have tried to sketch some illustration, not sure if it helps. :)
Because the pins are probably simply connected to DC electric motor, likely neither polarity won't destroy the gyro and incorrect connection will then result in opposite indication. But of course, I can not know for sure if there is any mechanical or electrical detail which would cause (immediate) damage when reverse-powered.
Related: perlanproject.org (composite wings and unpowered glider -- climbing up from low altitude though), stall speed is somewhat higher, just under 40 kts, but still subsonic at 100,000 ft and 76 thousands feet already reached. It can be good reading for information on high-altitude flight.
@CharlesBretana Of course, accept the answer which works best for you. I have seen JZYLs answer in middle of my writing, but wanted to post my one too, so there can be another explanation in different words.
