Why would you do that? Honestly, I am having a hard time getting a grasp on the logic of pulling hair out to hide an external overflow...

I do get it, however...
You can slide a sheet of black glass in there, if you seal all four edges, water will not likely get behind it (silicone sticks to glass better than any plastic) But I think you may have trouble finding black glass at a reasonable cost, aka a thin sheet of black glass. Table top material, shower door material is what you will likely find easiest, but you have to grab it before it gets tempered.
You can paint the inside of the tank back glass, if you want to spend ~$300+ per gallon for a paint that will actually stick to the glass. You could do the same for the portion of the overflow that does not need to hold to the back glass, and use an oil base black rustoleum for the rest of the back.
You can have the tank rebuilt using a black glass back panel. I built a 325 with a black glass back panel, 1" thick...( I upcharged the client for insisting they were right, and added two lamps to the light module....1 would have sufficed, but two to keep the balance.)
(Remember that doing things like this, reduces the amount of light available in the tank.)
There is a thing called 'stage affect' which is the tendency for black objects on the stage to 'disappear.' An internal black C2C high up on the back of the tank, will 'disappear,' and your rock structure will obscure most of the view of the back panel, making things blend together...the only light that will get 'blocked' would be at the back of the tank, (not nearly as much as one would think due to reflectance from the back panel) but there shouldn't be rock/life in the back 4" of the tank anyway, other than free swimming.
If you are not inclined to be diligent in keeping the back glass free of coralline, all of this is moot anyway.