I have 3 Game Gears and all of them have screen and sound issues. I fixed the sound on one of them. These things tend to break. I reckon you'll have a hard time getting lucky and finding a fully working one at a flea market for $10.
I don't even like portable consoles. I'd kill for a way to connect real Game Gear hardware to a TV or larger monitor, since I just can't enjoy emulation, knowing that it's emulation. Actually, I think I did find an article online once about someone who managed to mod a Game Gear for this purpose, but it was way way too serious an operation for my taste.