If the main mechanic is centered around aducity (vergänglichkeit)/water loss, the „action mechanics could be, too.
- There are given paths through the desert, like a road through a forest. Leaving that path will cost you time, and put you in greater danger, but maybe you discover something valuable? Risk vs. Gain
- If progress is the natural behaviour against loss over time, maybe standing stil will make you listen to traps or hidden treasures? Again, Risk vs. Gain
- Maybe standing still even puts you at danger. Are robbers tracking your path, will they catch up if you stop here? Can you see them at the horizon?