Can anyone provide a rules quote or reference (preferably, one that doesn't concern TWF)
Here's a
Rules of the Game article introducing TWF basics, in which the definition of "off-hand" is cited from the PHB p311, which I believe is the definition that Aluvial referenced upthread.
Here's the full text, with an interesting bit underlined:[sblock] (from
Rules of the Game at WotC's site)
Off Hand, Off-Hand Weapon:
When attacking with two weapons, the character must designate one of his hands as his off hand; the weapon held in that hand is treated as his off-hand weapon. The game rules don’t really care about whether you’re right-handed or left-handed, and it’s even OK to change your off hand designation from one round to the next.
Attacks with the off hand take a -4
penalty on the
attack roll (see page 311 in the
Player's Handbook) and only half the character’s Strength bonus (rounded down) applies to damage from the attack. Fighting with a weapon in each hand brings even bigger penalties.
When a character fights with a weapon in each hand, the weapon held in the off hand is called the off-hand weapon.
[/sblock]They say it's ok to switch off-hand designation between rounds, but they don't indicate why by RAW. This, indeed, supports the "no penalty for wielding two weapons (as differentiated from TWFing)" camp, as Desert Gled noted upthread (his "Side A").
Also, from the
3.5 FAQ, they say nothing prevents a character from declaring a shield as the primary weapon, in which case the weapon becomes the secondary:[sblock] (From the
3.5 FAQ)
Can a character make a shield bash attack using the shield as a primary weapon or can it be used only as an offhand weapon?
While the rules describe a shield bash as an off-hand weapon, that’s simply an assumption (that your primary hand is holding a weapon). There’s nothing stopping you from declaring your shield bash as your primary weapon. Of course, that means that any attack you make with your other hand becomes a secondary weapon. [/sblock]
I'll take all that as an "official" ruling: a character can freely switch off-hand designation between rounds. It's not really logical, but this is D&D

And it's certainly simpler that way.
However, I think also it's reasonable at a minimum to enforce off-hand on a
per round basis, which impacts AoOs. I'll phrase it something like this:
A character can generally change off-hand designation each round, but that designation stays in effect for the full round. Thus, an AoO made with the off-hand designated for that round is made with off-hand penalties (-4 attack, +1/2 STR damage.)