Well, I'm not sure this qualifies as a "local custom" but one thing which is special about Mizpe Ramon is the proximity of the desert wild life. Several years ago someone had found an exhausted leopard resting on the stairs. While this is really rare due to the small number of leopards, it's much easier to see some wild ibexes grazing on someone's back yard.
Ibexes are not afraid of humans and you will see soon the photos to prove it.
Also is home of the griffon and other birds of prey.
Before the sunset ibex go out and start looking for food and water, or when you have a sandstorm and there are only 3 strange humans around ;-)
See the scultures that you can find outside the national park, showing aprt of the daily life of the city.
We found simialr to this ones, all along the negev while driving down to Eilat.