the Mikvah is covered by a roofed structure (Connection Els!!)
I even had a photo of it (mikvah+cover) from my visit, weird that I did not 'make' the connection.
What I recall from my visit is that the site is really enclosed indeed, and also within a densely built-up town area. We need a volunteer to go (look out from all museum windows) and test it. The other way around (from the Cathedral) I will add already to the connection, the core zone also covers the modern building.