This can be completed after you get the Rooster artifact in Attila's Tomb.
Once in possession of the rooster, head back to the "Brimstone Forest - Village" fire pit and enter the basement of the house where you moved the altar with the feather.
Straight ahead on the right of the skinnier hallway is a bookshelf, press the book to open the secret door and reveal the light spring. Use the vial of light to find the secret word seal which is in one of the rooms in the basement.
When you have that, head over to the mine and enter. The first room straight ahead once at the bottom has the door for the light seal. Use it, then use the Rooster on this newly opened hole. Now go around the corner and use the rooster on the other hole exposed by sliding the altar to the side with the feather.
Once you've sent the rooster through both holes, the gate containing a chest, pile of gold, and your letter will be opened!