A gil seller is someone that tries to make real life money using something that is free to obtain and time. <-This is the supply.

One who buy from such individuals are rich (or obsessive/disturbed/need psychological attention) and want to use their surplus (hopefully) of money as a shortcut from the normal masses (you may call it laziness or the now common "I got no time to play, so I will pay"). <-This is the demand.

The supply can't exist unless there is demand. Breaking the chain by trying to prevent gil selling will not result in any actual reduction of gil selling. Stopping the supply would require humanity as a whole to be intelligent (sorry, not happening in this millennium). The only way to permanently stop gil sellers is to bypass them. SquareEnix would need to sell gils themselves, thus resulting in an official price for gil, which would lower profit of gil sellers and make their reputation at stakes (why buy from obscure sources when you can get it official?). Doing so would completely destroy the game's economy and allow players to rush through content even faster, making it simply impossible for SE to keep up the content unless they use radical grinding required content, which would lead to non-official sellers to rise up again.

Alternative? Prevent mindless chat spamming by disabling pasting in the chat box (no pasting = need to retype everything each replies). Remove paste option and the volume of messages a single person can produce will drop fast. A gil seller's spammer job will be harder. Harder job means more work, which means less profit. Less profit means the act of selling gils will be unattractive while ingame.

Simplicity is the key. Gil sellers are not what is to be addressed, but their ability to prevent others to enjoy their game by over filling shout chat with SPAM.

By the way, preventing pasting in a text box is really easy and quick while programming.

My opinion,
Lloyd Shade