Which piece of equipment is most essential when searching for a previously established monument?

When searching for a previously established monument, having a shovel is essential because it allows the survey technician to dig around potential monument locations to uncover buried markers. Monuments can sometimes be obscured by vegetation, soil, or other debris, and a shovel provides the necessary means to clear away these obstacles effectively.

In contrast, while the other equipment mentioned may have their uses, they do not serve as directly in locating a buried or hidden monument. For example, a measuring wheel is more useful for taking distance measurements and may not help in finding monuments that are not visible. A theodolite is primarily for measuring angles and would not assist directly in locating a monument that is not visible. A GPS device can help identify general locations based on coordinates but relies on the monument being known and documented previously. Hence, none of these tools can match the practicality of a shovel in the field when it comes to uncovering hidden or obscured markers.