What are the Halachot of Tznius as they relate specifically to men. Not men in relation to women. In other words, I'm not looking for "Men must act in a certain way when around women," I'm looking for "Men should act a certain way regardless of whom they're with."
see the Rama in the beginning of Orach Chaim which says one must feel constantly abashed in G-d's presence. These are the words of the More Nevuchim part 3 chapter 52, see there, and see also later on, and the Sefer Chasidim siman 35 (from Marpe Lenefesh commentary of shaar yichud ch.10)