Sounds like possibly a faulty fill valve in the toilet. get a Fluidmaster brand fill valve. It'll only cost about 10-12 bucks to find out if that's it, but it sounds like it. If it's already got a Fluidmaster, replace the rubber seal (bout 2 bucks).
Either that, like Lightfoot mentioned; or, since it is inside the wall, I was thinking it would be water-hammer. If that is the case then you install a water hammer ball-type valve in the pipes to absorb the vibration.Then again , I could be wrong. Whenever I hear plumbing noices, I think about water-hammer.