  We compute the four-point correlator of two gluon light-ray operators and two
gluon primaries from the four-gluon celestial amplitude in $(2,2)$ signature
spacetime. The correlator is non-distributional and allows us to verify that
light-ray operators appear in the OPE of two gluon primaries. We also carry out
a conformal block decomposition of the terms involving the exchange of gluon
operators.
