As per my observation, it has three states (Steam version 1.057M).
At the beginning, it's almost sunk, meaning you haven't completed the game.
After getting into the flying elevator at the end and restarting over (you have to load the last save data to see), the statue rises above the water and the lamp is flickering.
After 100% completion (523 +135 +6, plus all audio logs), the lamp stops flickering and dies out.
I am unsure about the second bullet, but I am extremely confident that the last point is correct, because I spent 3 hours tracing my last puzzle and my last audio log, and when I found them both, the lamp stopped flickering (I found the puzzle first, but the lamp was still flickering after solving it, it's the audio log that finally made the lamp went out).