<worn on finger> ring
<worn on finger> ring
<worn around neck> cloak
<worn around neck> cloak
<worn on body> shirt
<worn on head> skull
<worn on legs> pants
<worn on feet> boots
<worn on hands> gloves
<worn on arms> sleeves
<worn about body> cloak
<worn about waist> belt
<worn around wrist> bracer
<worn around wrist> bracer
<dual wield> sword

With this equipment I beleive I should be getting backfist attacks* but I don't beleive that I do. If the check is still there, but I've just been unlucky, please excuse me for being stupid.

(*) An assassin with this skill is able to take advantage of openings in their foe's defenses more readily, gaining additional strikes in combat as long as they have at least one hand free of encumberances.<-- leads me to beleive this qualifies.

>With this equipment I beleive I should be getting backfist
>attacks* but I don't beleive that I do. If the check is still
>there, but I've just been unlucky, please excuse me for being
>stupid.
>
>(*) An assassin with this skill is able to take advantage of
>openings in their foe's defenses more readily, gaining
>additional strikes in combat as long as they have at least one
>hand free of encumberances.<-- leads me to beleive this
>qualifies.

By design. If you are dual wielding anything, you won't get a backfist attack.