  We consider the time-dependent analysis of $B_d\to K_S\ell\ell$ taking into
account the time-evolution of the $B_d$ meson and its mixing into $\bar{B}_d$.
We discuss the angular conventions required to define the angular observables
in a transparent way with respect to CP conjugation. The inclusion of time
evolution allows us to identify six new observables, out of which three could
be accessed from a time-dependent tagged analysis. We also show that these
observables could be obtained by time-integrated measurements in a hadronic
environment if flavour tagging is available. We provide simple and precise
predictions for these observables in the SM and in NP models with real
contributions to SM and chirally flipped operators, which are independent of
form factors and charm-loop contributions. As such, these observables provide
robust and powerful cross-checks of the New Physics scenarios currently
favoured by global fits to $b\to s\ell\ell$ data. In addition, we discuss the
sensitivity of these observables with respect to NP scenarios involving scalar
and tensor operators, or CP-violating phases. We illustrate how these new
observables can provide a benchmark to discriminate among the various NP
scenarios in $b\to s\mu\mu$. We discuss the extension of these results for
$B_s$ decays into $f_0$, $\eta$ or $\eta'$.
