Query for areas/relations containing private ways

Hi, I would like to find gated communities in Argentina. Thus far, I have been able to filter the ones which are explicitly tagged as such, i.e. those with the tag residential=gated. This is the query I have used:

{{geocodeArea:Argentina}}->.searchArea;
(
  nwr["landuse"="residential"]["residential"="gated"](area.searchArea);
  nwr["landuse"="residential"]["barrier"="fence"](area.searchArea);
  nwr["gated_community"="yes"](area.searchArea);
);

However, there are several places which are not tagged in this way, but I know that are gated communities, like this place.
In this particular case, and in many others, I see there are ways inside tagged as access=private (e.g. this way).
Hence, my question is how can I search for areas which contain ways tagged like this?

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Just in case, I asked this same question in GIS Stackexchange and the answer worked for me.