CII line intensity mapping (LIM) is a potential technique to probe the early galaxies from the Epoch of Reionization (EoR). Several experiments e.g. CONCERTO, TIME, CCAT-p are underway to map the CII LIM signal fluctuations from the EoR, enabling us to estimate the CII power-spectrum and CII$times$21-cm cross-power spectrum. Observed LIM signal will have its time evolution embedded in it along the Line of Sight (LoS) due to the finite travel time of the signal from its origin to the observer. We have investigated this so-called light-cone effect on the observed statistics of our semi-numerically simulated CII signal from the EoR. Using a suit of simulated CII and neutral hydrogen 21-cm maps and corresponding light-cone boxes, we have shown that the light-cone effect can impact the CII power spectrum by more than 15% at large scales ($ksim 0.1, text{Mpc}^{-1}$, at $z=6.8$). We have also observed that the impact of light-cone effect on the CII power spectrum drops with decreasing redshift within the redshift range considered here ($7.2 lesssim z lesssim 6$). The CII$times$21-cm cross-power spectrum is also affected by light-cone, and in our models where reionization ends before $z=6$, we find that the maximum impact on cross-power can reach up to 20%. At $z=6.4$, we find comparatively pronounced variation in the light-cone effect with reionization history on the cross power. Faster reionization histories have a more drastic light-cone effect on cross-power. We conclude that we need to incorporate the light-cone in order to properly model the signal, constrain the EoR-related astrophysical parameters and reionization history using the CII$times$21-cm cross-power spectrum.
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