Synod Researchers appear in the Dwemer Ruins of Mzulft during the quest "Revealing the Unseen." They were part of an expedition led by Paratus Decimius and Gavros Plinius. By the time the Dragonborn enters Mzulft in search of answers to the Staff of Magnus all but Paratus have been slaughtered by Falmer. Gavros can be found dying at the entrance to Mzulft and manages to gasp something about Paratus and the Oculory before expiring. The Dragonborn then fights through legions of Falmer and recovers a certain Focusing Crystal from one.
They can only be found dead in Mzulft, either killed by Falmer or the various Dwarven traps. They all carry the same loot: Leather Boots, Blue Mage Robes and leveled daggers. (There are a total of ten Researchers during "Revealing the Unseen," and decreases to eight after the quest is finished.)