The far eastern room in the mine has a lever socket on the floor, where you can place the lever handle from a chest to the far south in order to open a storage room with a chest and a couple crates.
Heading south from the entrance and then west, there is a room with a pressure plate on the wall to open another storage room. Facing south at the end of the room, towards some curtains, the plate is on the left. Inside the storage room (behind some crates) a switch will open another wall, and close the one you just went through; jump onto the table and you can reach the pressure plate to open the wall again.