I lived in Arizona for ten years and saw many "objects" like that, and eventually discovered that the same phenomenon that causes a "mirage," also causes headlights, building lights, traffic lights - basically any light, to be reflected off of the desert surface back up to my point of view to appear as if it is "floating" above the ground, moving one way or another, suddenly disappearing and moving extra-ballistically as the light is obscured by objects and the reflection base is changed by the light moving - as in headlights.

I have also noticed videos of what appear to be lights outside of aircraft in which when the aircraft banks slightly, the light moves in tandem, which is what happens when a light source from inside the aircraft is reflected off the window back inside as if it is outside.