In response to this dreadful break, I would like to submit reasonable explanations for eyepatch!Brainy's eyepatch. (Aside from, of course, the generic "injury in battle.")
The result of accepting a dare from Alex in a drunken Superfriends game of Truth or Dare.
Testing out a couple's Halloween costume idea with Nia
Hiding the results of Winn getting him with the classic eyepiece prank until he could wash it off.
Trying to cheer up Kara with wholehearted participation in "Talk Like a Pirate" day.
Testing out some piece of tech he designed to augment J'onn's abilities.
His way of making clear that he is ignoring whatever poor agent sits beside him at the DEO.