Maybe not a pee mechanic, but maybe you could have plays "behind someone's back" - when someone isn't in the room, off to the loo or maybe refilling the bottle, you could do something against him in the comittee.
The glasses mechanic sounds really interesting, and made me think about liquid as representative of emotional state, and about sharing those emotions: when I have strong feelings towards you, I might give you some of my drink, or we could drink together, and when one is drinking all his glass, he is filling himself with emotion. Maybe something with turning your glass upside-down, blocking yourself from being filled from other players or the situation (the GM).
How about allowing players to "spike" a drink, by dropping a token in the glass? (The token would neeed to be clean and not easily swallowed!) If your drink is spiked, you get a mechanical "side effect" if you drink from the glass.
OK, so I was a litt afraid of the pee break mechanic suggestion of the previous page, but then it occured to me, that the pee break is when the Committee could have the ability to evaluate your fluids - everything from your pharmachology to your physiology to your hormonal activity can be measured in such a visit. Think THX or the Island for this one.