"I'm not lefthanded, either!"
One of the things my players benefit in having a DM who really is ambidextrous is that I probably undervalue the difficulty of Ambidexterity. I allow it as a handnedness roll (1% chance) and I allow players who are ambidextrous to have it automatically (although I very rarely give it to my own PCs for free) if they desire (for handedness in my setting, a character's PC can either match his own, or he may roll randomly.)
Ambidexterity is a Weapon Proficiency, and unless you're a fighter, you probably don't have a slot to spare in those, so it only stood to reason that we needed a less-powerful, less combat oriented form for those of us using it for things other than fencing the Man in Black.
To that end, we created the Limited Ambidexterity proficiency, a two-slot general Non-Weapon Proficiency for those who wanted the non-combat form, as well as the one-slot general Non-Weapon Proficiency "Off-hand." Limited Ambidexterity is a "roll-less" Non-Weapon proficiency, that is it bestows an ability (Ambidexterity except for with weapons) that does not need to be rolled.
Off-hand is a one-slot general Non-Weapon Proficiency that allows you to pick any non-weapon-proficiencies and do it with your off hand-exclusively, without penalty. Like skills such as mirror writing, this indicates your character took the time to learn how to do the skill in this way.
Ambidexterity, Limited: A character with this proficiency is ambidextrous, as per the weapon proficiency, but cannot use it to wield weapons. If the character takes the ambidexterity weapon proficiency at a later date, the DM may choose to allow the player to regain an empty slot, as it renders this proficiency useless. This proficiency was primary designed for mages interested in being ambidextrous.
Off-Hand: The character may specify any one of his non-weapon proficiencies which may be done one-handed as being able to be done with his off hand (left for right handed individuals, etc.), without penalty. Typical off-handed proficiencies include writing, specific musical instruments and crafting proficiencies. Truly ambidextrous characters do not need off-hand.