The core is thought to be solid or immensely viscous. If anything settles it would be on the outer layer of the inner core. Gravity is about 4.3m/s^(2) here and the radius is about 20% of the whole earth. From seismic wave analysis the density of the inner core is 3% less than iron. This means most likely that it’s mostly iron and lighter elements. Gold isn’t lighter than iron but I guess there could be very small traces.