I'll add to this as well. The same issue occurs in Buscarron's Fold.

Platform: Both PCs = Windows 7 64 Bit
ISP: Comcast
Type of Internet Connection: Cable
Internet Connection Speed: 22 mbps down/3 mbps up
Date & Time: August 6, 2011, 20:00
Frequency: Frequent
Character Name: Shanoa Kikosho/Amaterasu Kasha
Race: Elezen/Lalafell
World: Rabanastre
Class/Skill Rank: Various classes and ranks
Physical Level: 50
Area and Coordinates: Buscarron's Fold 35, 43
Party or Solo: Both
NPC Name: N/A
Monster Name: N/A
In-Game Time: All times
Steps:
Since I control two characters, I was able to see this firsthand on each screen. I sat both characters on the stool. On one screen I was sitting yet my other character was standing next to the stool. The same for the other screen. I kept sitting and unsitting, occasionally it would work where both characters were sitting on screen but usually one would be glitched. After getting up, sometimes one character would stay glitched next to the stool, unmoving, despite me being able to move the character far away. Changing gear, which causes the character to blink, fixed the issue.

I also performed 2 tests with the help of a friend. I sat both characters down on the stools and then stood up. On Character A's screen, Character B's would remain glitched next to the stool. Character B would be able to freely move around and run away yet on Character A's screen, Character B would still remain. My friend was able to confirm with me that Character B was glitched on his screen as well. I then ran both characters to the north to the open clearing south of Tam Tara Deepcroft. I was unable to see Character B on Character A's screen despite Character B standing right next to Character A. I cast cures, protect, stoneskin, and shell on Character A with Character B yet Character B still remained invisible on Character A's screen. For the next test, I used my friend watching the glitched Character B at Buscarron's Fold. I then changed gear with Character B and looked at Character A's screen. What happened next made me laugh because apparently, Character B began running from Buscarron's Fold all the way to my location to the north. The entire time however, Character B was standing next to Character A. This glitch seems to be random since it would occur with either character, elezen or lalafell.