Never mind, I got to reproduce it (didn't do it in FF6A, but if the code hasn't changed here, that shouldn't be shocking).
If your inactive party is in the same section near the Red Dragon, and you get tagged by it.. after fighting the boss, you are "displaced" out of your body. You can control the "invisible character" until you fight another enemy, switch parties, or goto the menu.
There you go, a movie of it:
http://rapidshare.com/files/140087672/ff3hack4bug.7z.htmlIt uses the awful Eternal Crystals hack, but you can reproduce this in a normal game. I've included the hack for convienence.
I doubt it has to do with having two parties.. but when you compare this to the Narshe battle, the only actual difference is that you get a message box that pops up that tells you the number of dragons left. When an inactive party is facing a monster, it fades out and switches back to the previous party you are controlling. The message box probably interrupts this, and causes the effect described.
We have EVEN MORE themes now, but some old ones are gone...