cncpc - yes a bright light will tend to shut down the goggles if you look straight at it. However, the light isn't pointing at you all the time, it is rotating, and you can look away if required.
If the cloudbase as reported was at 300' and the rock is 300' high, the lighthouse will have been in cloud anyway, significantly attenuating the strength of the beam.
SAS - in answer to an earlier question, yes, SAR crews will have a working knowledge of the lighthouse idents in their local area.