  Quantum localization (single-body or many-body) comes with the emergence of
local conserved quantities -- whose conservation is precisely at the heart of
the absence of transport through the system. In the case of fermionic systems
and $S=1/2$ spin models, such conserved quantities take the form of effective
two-level systems, called $l$-bits. While their existence is the defining
feature of localized phases, their direct experimental observation remains
elusive. Here we show that strongly localized $l$-bits bear a dramatic
universal signature, accessible to state-of-the-art quantum simulators, in the
form of periodic cusp singularities in the Loschmidt echo following a quantum
quench from a N\'eel/charge-density-wave state. Such singularities are
perfectly captured by a simple model of Rabi oscillations of an ensemble of
independent two-level systems, which also reproduces the short-time behavior of
the entanglement entropy and the imbalance dynamics. In the case of interacting
localized phases, the dynamics at longer times shows a sharp crossover to a
faster decay of the Loschmidt echo singularities, offering an experimentally
accessible signature of the interactions between $l$-bits.
