  It is known that Josephson junction (JJ) hosting scattering centers with
energy-dependent scattering amplitudes which breaks the
$\omega\rightarrow-\omega$ symmetry (where $\omega$ is the excitation energy of
electron about the Fermi level) exhibits finite thermoelectric response. In
contrast, here we show that even in a ballistic JJ this symmetry is broken and
it leads to a non-zero thermoelectric response when the junction length is of
the order of coherence length of the superconductor and the corresponding
thermoelectric coefficient confirms to the universal sinusoidal dependence on
$\phi_{12}$, where $\phi_{12}$ is the superconducting phase bias. In presence
of multiple scatterers in the junction region, we have numerically shown that
the sign of the even-in-$\phi_{12}$ part of the thermoelectric coefficient
fluctuates violently from one disorder configuration to another hence averaging
to vanishingly small values while the odd part tends towards the universal
sinusoidal dependence on $\phi_{12}$ as we approach the large disorder limit
under disorder averaging.
