The Evernight Temple is a vast island that is a part of the Enkanomiya Islands. You can see various ruins on the map with some of them requiring puzzles to solve. Here is how you can remove the barrier in the Evernight Temple ruin.
Use the central teleport waypoint in the Evernight Temple and go southwest until you see some ruins surrounded by a yellow emanating light. This light is a barrier preventing you from going inside the ruins.
To your left, you will see a mechanism that can change Evernight to Whitenight and vice versa. Switch to Evernight and you will see a glowing blue tree near the blue triangular statue.
Head towards it and when you get the blue light quickly change back to Whitenight.
After switching back to Whitenight, go towards the statue and the blue triangle will spawn on top of it.
Hit the blue triangular statue once and go to the white glowing tree. Get the glowing white light and run to the right side of the ruins.
You will see another mechanism here that changes to Evernight. Switch back to Evernight and go to the left side of the ruins. Hit the blue triangle here once and it will open the ruins.
The ruins will then reward you with a precious chest for your efforts!