How can I recreate this overexposed effect from the last scene in 'The Lighthouse'?
You can tell by the shadows that light's illumination was increased. However, you can acheive a similar result (though not perfect) by just keyframing the 'Curves' effect in After Effects. (I had better results with 'Curves' as opposed to 'Levels') See below: 





The curves were keyframed from default to: 



The top point is to blow out the whites, the middle point lifts the greys slightly and the bottom point keeps the blacks from getting brighter. 

Now, you'll notice that this has lifted the red values a little more than I'd like. This could then be fixed with a 'Tint' effect or by bumping the saturation way down with a 'Hue/Saturation' effect. Or even by messing with the individual RGB colours within the existing 'Curve' effect.