Who may sponsor or bring the family member, and what immigration/citizenship status must that person hold?
The procedure page states that the mechanism can be requested by Uruguayan citizens, legal residents or residents whose residence is in process, for persons who by their nationality require a visa to enter Uruguay. The decree quoted on the same page states that reunification may be made with a family member who is a permanent resident or whose residence is in process, who has presented means of living in legal form and who gives express consent. The two texts do not use the same wording, and the official source does not state whether a temporary legal resident may act as sponsor.
See recorded sources
Limits of the record- The two texts do not use the same wording, and the official source does not state whether a temporary legal resident may act as sponsor.