Investigating the Gunn-Peterson trough of high redshift quasars (QSOs) is a powerful way to reveal the cosmic reionization. As one of such attempts, we perform a series of analyses to examine the absorption lines observed with one of the highest redshift QSOs, PSO J006.1240+39.2219, which we previously discovered at z = 6.62. Using the Subaru telescope, we obtained medium-resolution spectrum with a total exposure time of 7.5 hours. We calculate the Ly$alpha$ transmission in different redshift bins to determine the near zone radius and the optical depth at 5.6$<$z$<$6.5. We find a sudden change in the Ly$alpha$ transmission at 5.75$<$z$<$5.86, which is consistent with the result from the literature. The near zone radius of the QSO is 5.79$pm$0.09 $p$Mpc, within the scatter of the near zone radii of other QSOs measured in previous studies. We also analyze the dark gap distribution to probe the neutral hydrogen fractions beyond the saturation limit of the Gunn-Peterson trough. We extend the measurement of the dark gaps to 5.7$<$z$<$6.3. We find that the gap widths increase with increasing redshifts, suggesting more neutral Universe at higher redshifts. However, these measurements strongly depend on the continuum modeling. As a continuum model-free attempt, we also perform the dark-pixel counting analysis, to find the upper limit of $langle x_{rm H I} rangle sim$0.6 (0.8) at $z<$5.8 ($z>$5.8). All three analyses based on this QSO show increasingly neutral hydrogen towards higher redshifts, adding precious measurements up to z$sim$6.5.
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