Our cat's litter box is in the basement. We keep a shoe in the door to keep it from closing but occasionally, the basement door closes and latches. The cat knows how to open the door if the latch isn't caught, so I tried to look for a mortise lock, set where the latch can be toggle to stay recessed until untoggled. I couldn't find anything. This is what our current locks it looks like.
So I need some thing that has the same profile but has the feature to keep the latch recessed.
I'm open to alternate solutions if anyone has any.