I don't know what the Valencian Cloth mystery means, but to my knowledge, the only time you can get that window frame is before the Black Dragon has woken up, so before the Dragon Quests, and before Home Marbule is restored. You obtain it from the blue NPC past the entrance to Marbule.
I tried it out with various savegames:
- After watching Nikki's Concert, and defeating all Lagoonates in Home Marbule, after the Black Dragon has been awakened, but before actually fighting it. I couldn't get the windowskin, the NPC would only say that the Black Dragon is awake.
- After watching Nikki's Concert, and defeating all Lagoonates in Home Marbule, after the Black Dragon has been awakened, and after fighting it. He still doesn't give the windowskin, he only says he can't believe you defeated the Black Dragon (or, if you enter with humans in your party, that he can't believe humans defeated the Black Dragon).
- Before visiting the S.S. Zelbess with Another Fargo in the party, and talking to Home Fargo, which triggers the entire Marbule thing. Before I did this, I could enter Another Marbule, and the blue NPC would simply say welcome and he gives you the windowskin as a welcome present. Still, this only applies with non-humans in your party, because if you have humans, he simply says he has nothing to say to humans. This same thing applies to after watching Nikki's Concert, the only important variable is that you can't defeat all the Lagoonates in Home Marbule.
So, in reality, this window frame can only be obtained during the time you're in Lynx' body, before or after you trigger Nikki's concert, but before you purge Home Marbule of the Lagoonates. Once you've killed all the Lagoonates, causing the Black Dragon to wake up, you can't get this anymore. After the visit to Home Fort Dragonia (or Chronopolis) the blue guy returns to his usual dialogue, but by then you also can't get it anymore since you have Serge's human body.
I hope this clears it up.