I love the idea OP (I've proposed it myself as well) It wouldn't necessarily need to be player-sold items either - It would sell a variety of server-generated items, all of different values and rarities, and would be running non-stop.

A player who wanted to sell via the Action House could buy a slot for a fee (15k maybe), and then their item would show up for others to bid on, with the profits or item going back to the player depending on if it sold.

As a player, I would love fun to sit there an watch for crazy deals to come up on anything from a stack of Ice Crystals to a Fire Materia III, to a pair of double-melded Darksteel Gauntlets