Looking at the 1929 Directory, Gorse Bank is on Morfa Drive, the entry follows the one for Dr Garretts Childrens Convalescent home and sanatorium which is listed as two properties - Min-y-Don and Holmfield - This was set up in the 1910's and consisted of several properties (up to 5) known collectively as Dr Garrets, - There are no entries for Morfa House or Holliewood house on this road in 1929 so it could be that by then they formed part of the Dr Garretts complex. There is a Morfa View, a Morfa Gardens House and a Morfa Cottage on the same road.
There is a lot of info on the internet about Dr Garrets which might help you and there is a collection of photos held at the Archives in Lloyd Street Llandudno