Follow the corridor filled with blue lights all the way to the end into a large circular room. Taijin’s Tower has floors very similar to this of which there are quite a few. Traversing them all and scouring every corner will take you quite some time but make the most of the enemies and items here.
The only enemies in this section are the Managarmr and they only come solo or duo. There are a few items here to collect, though, so head to the back wall and look for the Sphere there for a Sparkbane Brooch then check near the waypoint marker on the left side of the wall for 12x Chipped Fangs . Finally, you can find 4721 Gil next to a pillar.
Save if you wish then climb the stairs leading to the waypoint marker and board the elevator to the next floor.