This is something that has slightly bugged me. I don't really like looking at an empty slot on my character window and believe that every game should have a way to fill every character's equipment slot.
So far, that slot is only usable with Shields which only work on three character classes and the DotL and DotH classes. Why not allow the ones that can't use shields to have special items that can be placed in the off hand slot?
Take Arcanist, Summoner, and Scholar first. They all use Book like weapons. What does every book need? A Bookmark! Magical books shouldn't be an exception. These book marks can give a small boost to INT/MND/PIE or give added bonuses similar to what the Shields do.
Even if Bookmarks are a little odd, the Summoners and Scholars are always seen using Quills to write in the books. Bookmarks can be defensive off hands for Scholars while Quills could be offensive ones for Summoners.
Since SE doesn't give special effects to their items outside of stat boosts, I feel kinda deflated with giving out some extra bonuses though a lot could really benefit with general bonuses like, getting Arrows for Archers which change the element of their damage to match that of the Arrow. Arrows would not be consumed, it would be treated as all arrows that the Archer now carries are the same element and the one Arrow in the off hand slot would represent all the arrows the Archer carries.
Bards could carry Harps that, if SE allowed it, increase the support abilities of their songs, otherwise, it would just increase their own abilities that they need to focus on.
Monks and Pugilists, this one is a bit harder, but Monks are typically seen with Prayer Beads. I can't say what I see a Pugilist with as I haven't done much with them, but I can see them having the Prayer beads as well.
Dragoons and Marauders, now this one is interesting as their weapons are two handed. What I see for these two, are more like accessories. Special Dragon Fangs for the Dragoon and Bone fragments/trophies for the Marauder/Warrior. I'll have to play Marauder to learn more about them to give a better idea.
Could add Focuses for Thaumaturge and Black Mages as their Staves usually have some kinda focus stone to cast their magic. Conjurer and White Mages I can see with Idols when they don't have shields.
The only one I can't think of anything for is the Gladiator and Paladin as they require Sword and Shield by class default. I can't see them replacing the Shield as the off hand for bonus off hand equipment.
Other than Class specific, you can have Special Primal versions as well for the current Primals, though they'd probably fit better as an accessory just to allow the Gladiator/Paladin to use them.
I had a few examples, but forgot to write them down so when I think of some more I'll add them.