The Obligation of a Mezuzah on a Hidden Door / Zero-Line Door

Shalom, and thank you.
We are building several doors in our new home that are hidden doors, or zero-line doors. This means that the door has the form of a doorway, but there is no door frame or side posts, and it is integrated into the wall on all sides.
Assuming that these doors require a mezuzah because they have the form of a doorway, my question is where the mezuzah should be placed - on the wall within 3 handbreadths of where the form of the doorway is, or on the right side of the wall itself, where the mezuzah would have stood had the door had a frame.

Thank you very much