Pseudo force only when there is an acceleration.
Hence $T_0=T_1$ as there is uniform downward motion.
When it moves downward with a steady acceleration then pseudo force acts upwards, reducing net ' $g$ '
Since $T_2=2 \pi \sqrt{\frac{1}{g_{\text {net }}}}$
When $g$ reduces time period $T_2$ increases
$T_0=T_1 < T_2$
