This page of the guide to Far Cry 6 contains a detailed description of the The Mongoose and the Man Treasure Hunt available in Madrugada.
Subregion: Costa del Mar.
District: Lucero Lighthouse.
To start the treasure hunt, you must read the note attached to the wooden pole.
The entrance to the area is closed. This is no problem though, just shoot through the padlock.
Start the task by taking the key and opening the locker. A small "La Comadreja" animal will run out of it. Don't shoot it or you'll set the whole town on fire and scare everyone in the area.
After killing the animal, take the key, which you will use to explore the apartment.
Go back to the apartment and search it thoroughly. Once you open the large chest, the quest will end.