Sounds to me like the E string is rattling off the fret board. Try setting your bridge so that the height of action of the E string is 3 mm at the 12th fret. The G string action should be at 2 mm at the 12th fret, as factory specifications. Obviously, your can raise them higher if you prefer.
By all means do as Samataz suggests, and get someone to touch all sorts of parts to try to isolate that is buzzing. I, too, had a loose gear in a tuner machine, and it took weeks to try to isolate it. I even had it to a guitar maker - neither of us could isolate the buzz. It sound like it was coming from the bridge because that's where the sound of the strings come from! Does it do the same thing when tilted this way or that?
Not a Hofner, but.. One of the many annoying noises/rattles I had coming out of this old Gretsch was the tailpiece. I cured it by putting a small piece of moleskin on the tailpiece, where it bends over the body. You can't see it; doesn't hurt the finish; and that particular rattle went away. But, I also had loose wires rattling around inside the thing; loose tuner bushings; all kinds of things. And, most of them never sounded like they were coming from the actual location of the problem, either. My advice would be to check everything - very carefully...
