Stick a magnet on a telescoping stick up into the hole and catch the chain and pull it to basement.
drop the chain down the rest of the way to the floor.
Using a very light small chain, poke it through the camera hole and hopefully get it to fall to the cutout. Cut a section of drywall out about halfway up the wall - something like 12' x 12' (once you have a hole to patch, a larger one really isn't more work so you might as well make it a little larger so it's easier to work through). Drill a hole from the basement up into the wall. I think I would use very light chain for this and approach it this way. There are fiberglass rods that can be used but I don't see a way to get from the outside to the bottom plate without at least cutting a small hole in the interior drywall opposite the camera location.