I think the method of applying a damp cloth to the area and then turning the screen on would work,because I had a problem with stuck pixels on my Gameboy Advanced, and I tried that method, and it did the trick. Just keep in mind that it will be likely that you will have to disassemble the Gameboy to properly get to the screen, because of the plastic shield.
I’ve had that problem, and most likely the Game Pak and/or the pins in the Gameboy need to be cleaned. That, or just turn the Gameboy off and then re-insert the Game Pak.