Idea from JeanMarcHeneman
I think this is a really neat idea! It switches things up so one partner doesn't hog the keyboard (intentionally or unintentionally). The one thing I would be worried about is working "to beat the clock" - is the pressure beneficial or detrimental? I think I will suggest this to some of the guys at work.
An alternative that we're looking into is to use one of those anti-RSI (see RepetitiveStrainInjury) tools that lets you know how long you've been typing. It's easy for the member of the pair who's driving to lose track of how long they've been at the keyboard, leading to inadvertent hogging. This seems less obtrusive than a chess clock.
This sounds like an idea ripe for abuse, possibly written by someone who has never occupied the role TheCoach. Don't replace that role with a timer. Many XP Practices (including the teaching ones) remove the need to watch the clock. Don't add a new source of anxiety. --PhlIp
On the other hand, pairing is a skill that needs to be learned. Don't shun technological aids to learning merely because they'd be bad for you if abused. Also, don't use them to replace learning.
The OP suggested an experiment. Has anyone tried the experiment? How are we feeling today about shutting down ideas because they sounds a little weird?
See also: SandglassProgramming