There is another York House within St James's, I believe. Edward VIII lived there while prince of Wales. Is there a floor plan of where these private apartments are? I assume that the photo on page 1 that shows the garden of Clarence House with main St James's access must be more private apartments and not a part of the complex open to the public.
York House is one wing of the Palace, it overlooks Ambassador's Court and Cleveland Row so must be the rooms highlighted in light blue on this plan. Surprisingly given how many senior royals have lived there it is actually right at the front of the Palace alongside the road and not by the gardens at all.