I am not very familiar with vector tile schemas, but are you sure the information you want is actually present in the tiles at zoom 12?
I think many “small” features are omitted entirely at low zoom to reduce bandwidth and improve performance, so if the minor roads are getting stripped at an earlier stage then the style will not be able to enable something that just doesn’t exist in those tiles. If the tiles lack something you want then I think you will have to have them regenerated to start including them sooner.
If you are able to display the tiles in a wireframe/styleless view that might help determine what’s actually available for styling at each level.
