Why can't I find a stud in this wall?
The safest approach is to actually cut the wall open and see what you are really dealing with. While it involves drywall repair and paint, it also doesn't involve heavy fragile expensive items being hung based on conjecture. While the wall could be brick, it could also be studs (steel or wood) with resilient channel (somewhat age of building and local building practices dependent) - one of the features of resilient channel is better sound isolation, which is good for a party (common) wall. But some places a party wall is nearly always going to be 18" or more of masonry for fire purposes.

The wall shown here uses resilient channel, which is what I was looking for an image of, but also some other techniques that may well not apply.

You may find that you can "see" the resilient channel (or furring, as it may also be) better changing the studfinder direction (turn it 90 degrees, and sweep up and down)