That'* an easy one! That'* your stabilizer links jingling because they are loose. The noise
you are hearing are the washers on either side of the bushings hitting the metal part of
the link kit. My car had the ExACT same noise and I replaced my sway bar link kits and
no more noise. It affects the handling as well, I am sure you will notice a tighter ride and
crisper handling once they have been replaced.
The reason the mechanic cant find the loose part is because the weels are
hanging and the suspension is at the end of its travel on the hoist so everything is tight.