  Gravitational waves from supermassive black hole binary mergers along with an
electromagnetic counterpart have the potential to shed `light' on the nature of
dark energy in the intermediate redshift regime. Accurate measurement of dark
energy parameters at intermediate redshift is extremely essential to improve
our understanding of dark energy, and to possibly resolve a couple of tensions
involving cosmological parameters. We present a Fisher matrix forecast analysis
in the context of eLISA to predict the errors for three different cases: the
non-interacting dark energy with constant and evolving equation of state (EoS),
and the interacting dark sectors with a generalized parametrization. In all
three cases, we perform the analysis for two separate formalisms, namely, the
standard EoS formalism and the \textit{Om} parametrization which is a
model-independent null diagnostic for a wide range of fiducial values in both
phantom and non-phantom regions, to make a comparative analysis between the
prospects of these two diagnostics in eLISA. Our analysis reveals that it is
wiser and more effective to probe the null diagnostic instead of the standard
EoS parameters for any possible signature of dark energy at intermediate
redshift measurements like eLISA.
