Mexican carry...have not heard this term in decades, made me smile. A lot of detectives I knew in the wheel gun days used clip on holsters or "mexican carry". Some would wrap a thick rubber band or leather shoelace around the grip for traction. Many would also have the hammer cut so it would not snag in clothing. Some same side, some cross draw. If your carrying and not legal you could drop or stash the pistol in an emergency and not get caught wearing a holster..which tells you were wearing a gun. Undercover "narco" cops would do this also because almost no bad guy ever wears a holster.
I dont recommend it, but hey some times you gotta do what you gotta do at the time huh?