FAQ: Why can't I see Pivot in Object Properties
Pivot placement is not supported when the currently selected item is an "empty" object.
Meaning that the selected object is an empty object, and it has no mesh/polygons/surfaces and therefore can't have a material nor have an adjustable pivot because it essentially is only a pivot point.
Empty objects can be parents of mesh objects, which can sometimes lead to confusion.
No Pivot in Object Properties | Pivot in Object Properties |