  It has recently been demonstrated analytically that the two-point correlation
function for pairs of neutrinos may contain information about the size of the
proto-neutron star formed in a Galactic core-collapse supernova. The
information about the size of the source emerges via the neutrino equivalent of
intensity interferometry originally used by Hanbury-Brown and Twiss with
photons to measure the radii of stars. However the analytic demonstration of
neutrino intensity interferometry with supernova neutrinos made a number of
approximations: that the two neutrinos had equal energies, the neutrinos were
emitted at simultaneous times from two points and were detected simultaneously
at two detection points that formed a plane with the emission points. These
approximations need to be relaxed in order to better determine the feasibility
of neutrino intensity interferometry for supernovae neutrinos in a more
realistic scenario. In this paper we further investigate the feasibility of
intensity interferometry for supernova neutrinos by relaxing all the
approximations made in the earlier study. We find that, while relaxing any one
assumption reduces the correlation signal, the relaxation of the assumption of
equal times of detection is by far the largest detrimental factor. For neutrino
energies of order $\sim$15 MeV and a supernova distance of L = 10 kpc, we show
that in order to observe the interference pattern in the two-point correlation
function of the neutrino pairs, the timing resolution of a detector needs to be
on the order of $\lesssim 10^{-21}\;{\rm s}$ if the initial neutrino wave
packet has a size of $\sigma_x \sim 10^{-11}\;{\rm cm}$.
