That's actually one of the better takes on how to address the problem I've seen posted compared to the usual lottery/raffle suggestions (assuming SE isn't planning to overhaul the purchase system entirely).

Would effectively limit players to one "entry" per account since the character would still need to be at the placard in camp mode when the timer expires.

Addresses player's need to be able to move away from console/computer at times though does not release player to be doing other things in game. On the other hand it effectively forces players that prefer to just check at intervals so they can also do other things in game to enter camp mode.

Would players be free to enter/leave/re-enter camp mode so if someone wants to do something else then return they can?

How would you suggest addressing the gil part? Does the player need to have sufficient gil on their character to pay the purchase price to be able to enter Camp mode or would they have a short period to retrieve the gil once selected? (honestly not a fan of the latter with this system because then a player could camp with multiple accounts and trade the gil around only if they "win")