  Recent anisotropy studies of UHECR data at energies $\gtrsim$ 40 EeV, have
disclosed a correlation of their angular distribution with the extragalactic
local structure, specifically with either local starburst galaxies or AGN.
Using Monte Carlo simulations taking into account photo-disintegration
processes, we further explore a framework in which these UHECRs were
accelerated by Centaurus A in a recent powerful outburst before being scattered
by magnetic fields associated with local, Council of Giant, extragalactic
structure. We find that the observed intermediate scale anisotropies can be
accounted for by the Council of Giant structure imposing a response function on
the initial outburst of UHECRs from a single source located at Centaurus A's
position. The presence of these local structures creates `echoes' of UHECRs
after the initial impulse, and focusing effects. The strongest echo wave has a
lag of $\sim$ 20 Myr, comparable to the age of synchrotron-emitting electrons
in the giant Centaurus A lobes. Through consideration of the composition of
both the direct and echo wave components, we find that the distribution of the
light (1$<\ln A<$1.5) component across the sky offers exciting prospects for
testing the echo model using future facilities such as Auger prime. Our results
demonstrate the potential that UHECR nuclei offer, as "composition clocks", for
probing propagation scenarios from local sources.
