  We study the effect of introducing separable quenched disorder on a
non-equilibrium mean-field spin model exhibiting a phase transition to an
oscillating state in the absence of disorder, due to non-reciprocal
interactions. In the disordered model, the magnetisation and its time
derivative no longer carry the signature of the phase transition to an
oscillating state. However, thanks to the separable (Mattis-type) form of the
disorder, the presence of oscillations can be revealed by introducing a
specific, disorder-dependent observable. We also introduce generalised linear
and non-linear susceptibilities associated either with the magnetisation or
with its time derivative. While linear susceptibilities show no sign of a phase
transition, the third-order susceptibilities present a clear signature of the
onset of an oscillating phase. In addition, we show that the overlap
distribution also provides evidence for the presence of oscillations, without
explicit knowledge of the disorder.
