With Dark Souls: Remastered selected in your library, to the right of the play button, there should be symbols corresponding to Steam Cloud sync status, the date upon which you last played the game, your total play time, and your achievement progress. Further to the right of those symbols should be a cog/gear wheel symbol. Click it, mouse over the 'Manage' drop-down menu, and click 'Browse local files.' This should take you to the folder where Dark Souls: Remastered is installed.

Navigate to the folder labeled 'param' and then the folder within labeled 'DrawParam'. Inside should be files named aXY_DrawParam.parambnd.dcx and aXY_DrawParam.parambnd.dcx.prev

I suggest making a backup of all of these files as they govern the lighting behavior for the maps corresponding to the map codes indicated by aXY where XY is the internal map ID, but you can be lazy and just delete them all and then restore them from your recycle bin or verify game file integrity after you're done messing around with the broken lighting.

Regardless, delete these files to achieve the fullbright effect.

Important: DO NOT delete the files named default_DrawParam.parambnd.dcx and default_DrawParam.parambnd.dcx.prev or else the game will fail to load.

Now, when you launch the game, specular maps, baked lighting, dynamic light sources like the skull lantern, Cast Light spell, and Sunlight Maggot head piece will be disabled, and other things will be missing (visual effects are unaffected) and the game will look like a model you pulled up in Blender with the MatCap material applied to it. Particularly useful in dark areas (obviously though this is not the intended way to play the game and may cheapen the experience, but it could be fun to experiment with in NG+ or if you are a returning DS1 player.) There will also be a thick layer of fog in basically every area that's large enough.